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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

How to Solve Percent Problems? (+FREE Worksheet!)

Related Topics

  • How to Find Percent of Increase and Decrease
  • How to Find Discount, Tax, and Tip
  • How to Do Percentage Calculations
  • How to Solve Simple Interest Problems

Step by step guide to solve percent problems

  • In each percent problem, we are looking for the base, or part or the percent.
  • Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

  • \(51\) is \(340\%\) of what?
  • \(93\%\) of what number is \(97\)?
  • \(27\%\) of \(142\) is what number?
  • What percent of \(125\) is \(29.3\)?
  • \(60\) is what percent of \(126\)?
  • \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

  • \(\color{blue}{15}\)
  • \(\color{blue}{104.3}\)
  • \(\color{blue}{38.34}\)
  • \(\color{blue}{23.44\%}\)
  • \(\color{blue}{47.6\%}\)
  • \(\color{blue}{100}\)

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Mathematics LibreTexts

4.2: Percents Problems and Applications of Percent

  • Last updated
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  • Page ID 142718

  • Morgan Chase
  • Clackamas Community College via OpenOregon

You may use a calculator throughout this module.

sale-tag.jpg

Recall: The amount is the answer we get after finding the percent of the original number. The base is the original number, the number we find the percent of. We can call the percent the rate.

When we looked at percents in a previous module, we focused on finding the amount. In this module, we will learn how to find the percentage rate and the base.

\(\text{Amount}=\text{Rate}\cdot\text{Base}\)

\(A=R\cdot{B}\)

We can translate from words into algebra.

  • “is” means equals
  • “of” means multiply
  • “what” means a variable

Solving Percent Problems: Finding the Rate

Suppose you earned \(56\) points on a \(60\)-point quiz. To figure out your grade as a percent, you need to answer the question “\(56\) is what percent of \(60\)?” We can translate this sentence into the equation \(56=R\cdot60\).

Exercises \(\PageIndex{1}\)

1. \(56\) is what percent of \(60\)?

2. What percent of \(120\) is \(45\)?

1. \(93\%\) or \(93.3\%\)

2. \(37.5\%\)

Be aware that this method gives us the answer in decimal form and we must move the decimal point to convert the answer to a percent.

Also, if the instructions don’t explicitly tell you how to round your answer, use your best judgment: to the nearest whole percent or nearest tenth of a percent, to two or three significant figures, etc.

Solving Percent Problems: Finding the Base

Suppose you earn \(2\%\) cash rewards for the amount you charge on your credit card. If you want to earn $ \(50\) in cash rewards, how much do you need to charge on your card? To figure this out, you need to answer the question “\(50\) is \(2\%\) of what number?” We can translate this into the equation \(50=0.02\cdot{B}\).

3. $ \(50\) is \(2\%\) of what number?

4. \(5\%\) of what number is \(36\)?

3. $ \(2,500\)

5. An \(18\%\) tip will be added to a dinner that cost $ \(107.50\). What is the amount of the tip?

6. The University of Oregon women’s basketball team made \(13\) of the \(29\) three-points shots they attempted during a game against UNC. What percent of their three-point shots did the team make?

7. \(45\%\) of the people surveyed answered “yes” to a poll question. If \(180\) people answered “yes”, how many people were surveyed altogether?

5. $ \(19.35\)

6. \(44.8\%\) or \(45\%\)

7. \(400\) people were surveyed

Solving Percent Problems: Percent Increase

When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it’s it’s a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you wouldn’t care because it’s such a small percentage of the original price.

To find the percent of increase:

  • Subtract the two numbers to find the amount of increase.
  • Using this result as the amount and the original number as the base, find the unknown percent.

Notice that we always use the original number for the base, the number that occurred earlier in time. In the case of a percent increase, this is the smaller of the two numbers.

8. The price of a candy bar increased from $ \(0.89\) to $ \(1.39\). By what percent did the price increase?

9. The population of Portland in 2010 was \(583,793\). The estimated population in 2019 was \(654,741\). Find the percent of increase in the population. [1]

8. \(56.2\%\) increase

9. \(12.2\%\) increase

Solving Percent Problems: Percent Decrease

Finding the percent decrease in a number is very similar.

To find the percent of decrease:

  • Subtract the two numbers to find the amount of decrease.

Again, we always use the original number for the base, the number that occurred earlier in time. For a percent decrease, this is the larger of the two numbers.

10. During a sale, the price of a candy bar was reduced from $ \(1.39\) to $ \(0.89\). By what percent did the price decrease?

11. The number of students enrolled at Clackamas Community College decreased from \(7,439\) in Summer 2019 to \(4,781\) in Summer 2020. Find the percent of decrease in enrollment.

10. \(36.0\%\) decrease

11. \(35.7\%\) decrease

Relative Error

In an earlier module, we said that a measurement will always include some error, no matter how carefully we measure. It can be helpful to consider the size of the error relative to the size of what is being measured. As we saw in the examples above, a difference of \(50\) cents is important when we’re pricing candy bars but insignificant when we’re pricing cars. In the same way, an error of an eighth of an inch could be a deal-breaker when you’re trying to fit a screen into a window frame, but an eighth of an inch is insignificant when you’re measuring the length of your garage.

The expected outcome is what the number would be in a perfect world. If a window screen is supposed to be exactly \(25\) inches wide, we call this the expected outcome, and we treat it as though it has infinitely many significant digits. In theory, the expected outcome is \(25.000000...\)

To find the absolute error , we subtract the measurement and the expected outcome. Because we always treat the expected outcome as though it has unlimited significant figures, the absolute error should have the same precision (place value) as the measurement , not the expected outcome .

To find the relative error , we divide the absolute error by the expected outcome. We usually express the relative error as a percent. In fact, the procedure for finding the relative error is identical to the procedures for finding a percent increase or percent decrease!

To find the relative error:

  • Subtract the two numbers to find the absolute error.
  • Using the absolute error as the amount and the expected outcome as the base, find the unknown percent.

Exercisew \(\PageIndex{1}\)

12. A window screen is measured to be \(25\dfrac{3}{16}\) inches wide instead of the advertised \(25\) inches. Determine the relative error, rounded to the nearest tenth of a percent.

13. The contents of a box of cereal are supposed to weigh \(10.8\) ounces, but they are measured at \(10.67\) ounces. Determine the relative error, rounded to the nearest tenth of a percent.

12. \(0.1875\div25\approx0.8\%\)

13. \(0.13\div10.8\approx1.2\%\)

6509400855_aaaf915871.jpg

The tolerance is the maximum amount that a measurement is allowed to differ from the expected outcome. For example, the U.S. Mint needs its coins to have a consistent size and weight so that they will work in vending machines. A dime (10 cents) weighs \(2.268\) grams, with a tolerance of \(\pm0.091\) grams. [2] This tells us that the minimum acceptable weight is \(2.268-0.091=2.177\) grams, and the maximum acceptable weight is \(2.268+0.091=2.359\) grams. A dime with a weight outside of the range \(2.177\leq\text{weight}\leq2.359\) would be unacceptable.

dime-under-microscope-300x225.jpg

A U.S. nickel (5 cents) weighs \(5.000\) grams with a tolerance of \(\pm0.194\) grams.

14. Determine the lowest acceptable weight and highest acceptable weight of a nickel.

15. Determine the relative error of a nickel that weighs \(5.21\) grams.

A U.S. quarter (25 cents) weighs \(5.670\) grams with a tolerance of \(\pm0.227\) grams.

16. Determine the lowest acceptable weight and highest acceptable weight of a quarter.

17. Determine the relative error of a quarter that weighs \(5.43\) grams.

14. \(4.806\) g; \(5.194\) g

15. \(0.21\div5.000=4.2\%\)

16. \(5.443\) g; \(5.897\) g

17. \(0.24\div5.670\approx4.2\%\)

  • www.census.gov/quickfacts/fact/table/portlandcityoregon,OR,US/PST045219 ↵
  • https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications and https://www.thesprucecrafts.com/how-much-do-coins-weigh-4171330 ↵

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Solving problems with percentages

  • Price difference I
  • Price difference II
  • How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

Video lessons

A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?

Solve "54 is 25% of what number?"

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Solving Percent Problems

Percent Problems

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How to Solve Percent Problems? 13 Amazing Examples!

// Last Updated: January 20, 2020 - Watch Video //

Ratios and proportions help us in solving problems with percents .

Jenn (B.S., M.Ed.) of Calcworkshop® teaching percents

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Because a percent is the ratio (fraction) of one number to another.

In other words, its a number divided by 100.

What is most important to note is that our overall goal is to translate each problem into an algebraic expression by looking for keywords such as “of” and “is,” and then solve for the unknown variable.

First, we will look at how a percent is created by understanding it is simply a proportion:

How to use ratios and proportions to solve problems involving percents

Percents as a Proportion

And we will quickly see that most problems will follow a very simple Percents Formula, as Khan Academy so accurately states.

Together will look at how to change percents to fractions, percents to decimals, and decimals to percents for various problems.

Additionally, we will look at real-world examples, such as finding the percent of commission, the price of an item with a percent discount, change in population, as well as mixture problems.

Solving Percents (How-To) – Video

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Solving Percent Application Problems

Math: basic tutorials : solving percent application problems.

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Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem.

Example and Activity

What is the sale price of a coat that is normally 95 dollars and is discounted by 20 percent.

Line 1: What are you being asked to find. We are being asked to find the sale price.

Line 2: Choose a variable to represent it. Let s be the sale price.

Line 3: Write a sentence that gives the information to write an equation to find s. If the discount is 20 percent, this means the sale price is 80 percent of the original price.

Line 4: Translate the words into algebra, so the equation is s equals 0 decimal 8 0 times 95.

Line 5: Multiply to solve for s, so s equals 76.

Line 6: Write a statement that answers the question. The sale price of the coat is 76 dollars.

A cupcake contains 480 calories, and 240 of those calories are from fat. What percent of the total calories come from fat?

Line 1: What are you being asked to find? We are being asked to find the percent of the calories that from fat.

Line 2: Choose a variable to represent it. Let p be the percent from fat.

Line 3: Write a sentence that gives the information to find p. What percent of 480 is 240?

Line 4: Translate the words into algebra, so the equation is p time 480 equals 240.

Line 5: Divide both sides of the equation by 480 to solve for p, so the equation is 480p divided by 480 equals 240 divided by 480.

Line 6: Simplify to get p equals 0 decimal 5.

Line 5: Convert the decimal to a percent by multiplying by 100 percent so p = 50 percent.

Line 7: Write a statement that answers the question. Therefore, 50 percent of the calories in the cupcake are from fat.

Source: " Prealgebra - opens in a new window " by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

  • Summary: Solving Percent Application Problems - PDF - Opens in a new window This document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
  • Worksheet: Solving Percent Application Problems - PDF - Opens in a new window This document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
  • << Previous: Simple Operations with Percent
  • Next: Solving Percent Change Problems >>

Note: This material is meant as a general guide, if your professor's instructions differ from the information we've provided, always follow your professor's instructions. Also note, icons on this site are used through a Noun Project Pro license. Please be sure to provide proper attribution if you reuse them.

  • Last Updated: Aug 22, 2023 3:28 PM
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problem solving about percent

Solved Examples on Percentage

The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage.

Solved examples on percentage:

1.  In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.

Total number of invalid votes = 15 % of 560000

                                       = 15/100 × 560000

                                       = 8400000/100

                                       = 84000

Total number of valid votes 560000 – 84000 = 476000

Percentage of votes polled in favour of candidate A = 75 %

Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000

= 75/100 × 476000

= 35700000/100

2. A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.

Total number of fruits shopkeeper bought = 600 + 400 = 1000

Number of rotten oranges = 15% of 600

                                    = 15/100 × 600

                                    = 9000/100

                                    = 90

Number of rotten bananas = 8% of 400

                                   = 8/100 × 400

                                   = 3200/100

                                   = 32

Therefore, total number of rotten fruits = 90 + 32 = 122

Therefore Number of fruits in good condition = 1000 - 122 = 878

Therefore Percentage of fruits in good condition = (878/1000 × 100)%

                                                                 = (87800/1000)%

                                                                 = 87.8%

3. Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?

Solution:            

Let the money he took for shopping be m.

Money he spent = 30 % of m

                      = 30/100 × m

                      = 3/10 m

Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10

But money left with him = $ 2100

Therefore 7m/10 = $ 2100          

m = $ 2100× 10/7

m = $ 21000/7

Therefore, the money he took for shopping is $ 3000.

Fraction into Percentage

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Application of Percentage

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Education Next

The 5 Percent Problem

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Laurence Holt

Photo of a confused student holding a tablet

In 1924, Sidney Pressey, a professor from Ohio State University, invented a teaching machine. The mechanical device, about the size of a portable typewriter, allowed students to press one of four keys to answer questions curated by expert instructors. A later version dispensed candy for correct answers.

Education optimists were fascinated, and Pressey promised the technology would accelerate student learning. But the machine was a commercial flop.

Exactly a century later, similar programs spangle U.S. classrooms: i-Ready, DreamBox, Khan Academy, IXL, and many others. They are driven by clever algorithms rather than finger power. Though none feature candy dispensers as rewards, some have animations or videos explaining what a student got wrong. The pandemic mania for teaching kids on computers prompted a great surge in the adoption of such programs.

Do they work? In August 2022, three researchers at Khan Academy, a popular math practice website, published the results of a massive, 99-district study of students. It showed an effect size of 0.26 standard deviations (SD)—equivalent to several months of additional schooling—for students who used the program as recommended.

A 2016 Harvard study of DreamBox, a competing mathematics platform, though without the benefit of Sal Khan’s satin voiceover, found an effect size of 0.20 SD for students who used the program as recommended. A 2019 study of i-Ready, a similar program, reported an effect size in math of 0.22 SD—again for students who used the program as recommended. And in 2023 IXL, yet another online mathematics program, reported an effect size of 0.14 SD for students who used the program as designed.

Those gains, and many others like them reported each year, are impressive. Since use of these tools is widespread, one could be forgiven for asking why American students are not making impressive gains in math achievement. John Gabrieli, an MIT neuroscientist, declares himself “impressed how education technology has had no effect on . . . outcomes.” He was talking about reading but could equally have called out mathematics, the other big area in which education technology is widely used but growth in achievement has not followed .

A clue is in those wiggle words “students who used the program as recommended.” Just how many students do use these programs as recommended—at least 30 minutes per week in the case of Khan Academy? The answer is usually buried in a footnote, if it’s reported at all. In the case of the Khan study, it is 4.7 percent of students. The percentage of students using the other products as prescribed is similarly low.

Imagine a doctor prescribing a sophisticated new drug to 100 patients and finding 95 of them didn’t take it as prescribed. That is the situation with many online math interventions in K–12 education today. They are a solution for the 5 percent. The other 95 percent see minimal gains, if any.

Worse, some studies report that the 5 percent who do see results skew towards higher income, higher performing students. A 2022 study of Zearn, another math learning platform, in Washington, DC, public schools found that students who used the program most were more likely to be white or Asian and from high-income areas of the city and less likely to be considered at risk. (Other studies, including the one of Khan Academy, show no particular pattern across student groups.) Learning gains for any group of students are to be welcomed, but it may be that the 5 percent of learners who achieve strong results with these programs could achieve the same strong results with any practice program, including paper-and-pencil practice. At the very least, districts leaders who adopt online learning programs with the aim of reducing equity gaps in math should be aware that they may be widening them.

It’s not at all clear that the program vendors are at fault, any more than you would blame a pharmaceutical company for the failure to see results among patients who didn’t take their drug. Indeed, the vendors point to data that students who use their program more show higher performance. But that is a correlation. As Hilary Yamtich, a fourth grade math teacher at a school in Oakland, California, who conducted a study of her own, points out, “students who are more motivated to learn are more likely to choose to use Khan.”

There may be other reasons beyond motivation that some students use these programs to such different extents. One possibility is that some teachers are more committed to implementing the programs than others—if they selected the program themselves, for instance. And “programs that have been carefully integrated into the curriculum, rather than seen as supplemental to it, likely see more consistent usage patterns,” according to Sarah Johnson of Teaching Lab, a nonprofit focused on teacher coaching. The Harvard study of DreamBox found that the variation in student usage was driven more by “teacher- and school-level practices” than by “student preferences.”

A second theory focuses on student behavior: perhaps some students use the program at home while others do not. The pandemic forced many school districts to address disparities in access to technology, but not all students have parents who badger them to do their homework or have time to assist with it.

Other students may simply be more motivated to do well in math, as Yamtich says, or more assiduous in following their teacher’s instructions. Another Zearn study found that high-usage students were more likely to believe they can improve in math, an attitude researchers refer to as a “growth mindset.” The researchers concluded that using their program led to a better mindset, but the causal arrow could equally point in the opposite direction: students with a growth mindset invest more time in trying to improve.

Third, the programs may have been unintentionally designed to fit high achievers better, says Stacy Marple, a researcher at WestEd who has studied several online programs. Marple tells the story of a 7th grade classroom where she observed an online program that asked a student, “Using the principles of equivalency and inverse operations, isolate the variable” in an equation. The student clicked each possible answer in turn. “Do you know what [the question] is asking you?” Marple asked the student. “Umm, not really,” she replied. (Your correspondent is similarly unsure.) The program offered no way for students to look up the meaning of a word like “isolate.”

In another classroom, students were provided with video explanations of concepts they struggled with. But few students ever watched a video, since doing so was considered a “hint” by the program and resulted in points being deducted from their score. That, in turn, might result in them having to repeat a problem set from the beginning, What is meant to help students instead makes some feel like a bird in a box, which they are most desperate to avoid.

Whatever the reason for low usage—and it is likely a combination of all of these—schools should assume the impact of online learning programs will be limited unless they take steps to ensure the students who need them most get the recommended dosage. This is especially important since, as Ken Koedinger, an expert on education technology at Carnegie Mellon University, points out, there is solid evidence that the amount of practice a student does directly impacts their learning. Recognizing this, an initiative in Texas, for example, offered grants only to those districts that submitted a plan to achieve fidelity to a learning program and a way to track it. At the very least, districts should make a habit of looking at usage data from these platforms.

Since schools pay for these programs, it would be fair for taxpayers to ask if their dollars are being wasted. That could lead to schools seeking agreements with vendors so they pay only for time used. “Even better,” says Raymond Pierce, president of the Southern Education Foundation, a non-profit founded to advance education opportunities, “would be to pay solely for growth in student achievement.” That seems sure to focus the minds of vendors’ executives who can expect, on current performance, to lose their shirts.

Districts may have been lulled into a false sense of security by the research reports published by vendors. Federal rules for schools’ use of Title I funds in low-performing schools require them to purchase only interventions that have evidence of effectiveness for a sample of at least 300 students. But it says nothing about what percentage of the student body that 300 should represent. The urgent question is not just whether the tools are effective but for whom. One hundred years after Pressey, we still don’t know.

Laurence Holt is a Senior Advisor at XQ Institute and author of The Science of Tutoring .

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The Opening Days of Trump’s First Criminal Trial

Here’s what has happened so far in the unprecedented proceedings against a former u.s. president..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

It’s the first day of the Trump trial and just walking out the door in my house. It’s a beautiful day, 6:11 AM. The thing that keeps running through my head is it’s kind of amazing that hundreds of jurors are going to show up at the Manhattan courthouse. And some of them are going to know what they’re there for — probably talking to their friends, their relatives about it.

Some of them are going to learn this morning talking to other jurors in line, asking what all the fuss is about. But I really do imagine that there’s going to be at least one potential juror who, headphones on, getting into court. Here they’re going to be there for the first criminal trial of Donald J. Trump. And just, I mean, how would you react?

[MUSIC PLAYING]

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.” Today, what it’s been like inside the lower Manhattan courtroom, where political and legal history are being made? My colleague, Jonah Bromwich, on the opening days of the first criminal trial of a US President. It’s Thursday, April 18.

Is that his mic? Hi, there.

Hello. How are you?

I’m doing good.

OK. Thank you for coming in, Jonah —

Thank you for having me.

— in the middle of a trial. Can you just explain why you’re able to even be here?

Sure. So we happen to be off on Wednesdays during trial, so.

We being not “The New York Times,” but the courts.

That’s right.

Which is why we’re taping with you. And because we now have two full court days of this history-making trial now under our belts. And the thing about this trial that’s so interesting is that there are no cameras in the courtroom for the wider world.

There’s no audio recordings. So all we really have is and your eyes and your notebook, maybe your laptop. And so we’re hoping you can reconstruct for us the scene of the first two days of this trial and really the highlights.

Yeah, I’d be happy to. So on Monday morning, I left the subway. It’s before 7:00 AM. The sun is just rising over these grandiose court buildings in lower Manhattan.

I’m about to turn left onto Center Street. I’m right in front of the big municipal building.

And I turn onto Center Street. That’s where the courthouses are.

I’m crossing.

And I expected to see a big crowd. And it was even bigger than I had anticipated.

Here we go. Here we go. Here we go. Now, I finally see the crowd.

You have camera banks. You have reporters. You have the beginnings of what will eventually become a protest. And you have this most New York thing, which is just a big crowd of people.

[CHUCKLES]: Who just know something is going on.

That’s right. And what they know is going on is, of course, the first trial of an American president.

All right, I’m passing the camera, folks. Camera, camera, camera, camera. Here we go.

Let’s start with Sharon Crowley live outside the courthouse in Lower Manhattan.

I want to get right to ABC’S Aaron Katersky who’s outside of the courthouse.

Robert Costa is following it outside the courthouse in Lower Manhattan. Bob, I saw the satellite trucks lined up all in a row. Good morning.

Talk to us how we got here exactly.

So this is the case that was brought by the Manhattan district attorney. So prosecutors have accused Donald Trump of covering up the actions of his former fixer, Michael Cohen, after Cohen paid hush money to Stormy Daniels. Stormy Daniels had a story about having had sex with Donald Trump, which Trump has always denied.

Cohen paid her money, and then Trump reimbursed Cohen. And prosecutors say that Trump essentially defrauded the American people because he hid this information that could have been very important for the election from those people when he reimbursed Cohen.

Right. And as I remember it, he also misrepresented what that reimbursement was. Claimed it was a legal fee when, in fact, it was just reimbursing Michael Cohen for a hush money payment.

Exactly, yeah. He definitely didn’t say reimbursement for hush money payment to Stormy Daniels. It’s a cover up case. It’s a case about hiding information you don’t want people to see.

Right. And of course, the context of all this is that it is in the middle of a presidential election. It’s 2016. Trump wants to keep this secret, prosecutors allege, so that the American public doesn’t know about it and potentially hold it against him.

Right. And prosecutors are telling a story about election interference. They’re saying that Trump interfered with an election. And Trump himself is also using the phrase “election interference.” But he’s painting the trial itself as election interference as he now runs again in 2024.

Fascinating.

And because we’re in Manhattan, and because the jury pool is going to be largely Democratic, and the judge is a Democrat, and the district attorney is a Democrat, Trump keeps claiming he cannot get a fair shake. This is democrat central. And in democrat central, Trump doesn’t have a chance.

OK. So, what happens once you actually enter the courthouse?

Outside, there’s all this fanfare. But inside, it’s a little bit business as usual. So I go up to the 15th floor, and I walk into the courtroom, and I sit down, and it’s the same old courtroom. And we’re sitting and waiting for the former president.

Around 9:30, Trump walks in. He looks thin. He looks a little tired, kind of slumping forward, as if to say with his body like let’s get this over with. Here we go.

The judge walks in a little bit after that. And we think we’re all set for the trial to start, but that’s not what happens here. And in fact, there are a series of legal arguments about what the trial is going to look like and what evidence is going to be allowed in.

So, for example, prosecutors ask that they be allowed to admit into evidence headlines from “The National Enquirer” that were attacks on Trump’s 2016 opponents — on Ted Cruz, on Marco Rubio, on Ben Carson.

Because prosecutors are in some sense putting Trump’s 2016 campaign on trial. These headlines are a big part of that because what prosecutors say they show is that Trump had this ongoing deal with “The National Enquirer.” And the publisher would promote him, and it would publish damaging stories about his opponents. And then crucially, it would protect Trump from negative stories. And that’s exactly what prosecutors say happened with Stormy Daniels. That “The National Enquirer” tipped Cohen off about Stormy Daniels trying to sell her story of having had sex with Donald Trump, which he denies. And that led to the hush money payment to her. So what prosecutors are doing overall with these headlines is establishing a pattern of conduct. And that conduct, they say, was an attempt to influence the election in Trump’s favor.

And the judge agrees. He’s going to admit this evidence. And this is a pretty big win for the prosecution. But even though they win that one, they’re not winning everything.

They lose some important arguments here. One of them was that after the Access Hollywood tape came out, there were allegations of sexual assault against Donald Trump. And you know this, Michael, because you reported two of them — two of the three in question at this very trial.

Prosecutors had hoped to talk about those during trial in front of the jury to show the jurors that the Trump campaign was really, really focused on pushing back against bad press in the wake of the Access Hollywood tape in which Trump seemed to describe sexual assault. That was a big problem for the campaign. Campaign did everything it could to push back, including against these allegations that surfaced in the wake of the tape.

But the judge, saying that the allegations are hearsay — that they’re based on the women’s stories — says absolutely not. That is incredibly prejudicial to the defendant.

Interesting.

And that Donald Trump would actually not get a fair trial were those allegations to be mentioned. And so he will not let those in. The jurors will not hear about them.

So this is a setback, of course, for the prosecution, a victory for Trump’s legal team.

It’s a setback. And it also just shows you how these pre-trial motions shape the context of the trial. Think of the trial as a venue like a theater or an athletic contest of some sort. And these pre-trial motions are about what gets led into the arena and what stays out. The sexual assault allegations — out. “The National Enquirer” headlines — in.

OK. And how is Trump sitting there at the defense table reacting to these pre-trial motion rulings from the judge?

Well, as I’ve just said, this is very important stuff for his trial.

Right. Hugely important.

But it’s all happening in legal language, and I’m decoding it for you. But if you were sitting there listening to it, you might get a little lost, and you might get a little bored. And Trump, who is not involved in these arguments, seems to fall asleep.

Seems to fall asleep — you’re seeing this with your own eyes.

What we’re seeing, overall, including our colleague, Maggie Haberman, who’s in the overflow room and has a direct view of Trump’s face — I’m sitting behind him in the courtroom, so I can’t see his face that well.

You guys are double teaming this.

That’s right. I’m sitting behind him, but Maggie is sitting in front of him. And what she sees is not only that his eyes are closed. That wouldn’t get you to he is asleep.

And we have to be really careful about reporting that he’s asleep, even if it seems like a frivolous thing. But what happens is that his head is dropping down to his chest, and then it’s snapping back up. So you’ve seen that, when a student —

I’ve done that.

(CHUCKLES) Yeah. We all kind of know that feeling of snapping awake suddenly. And we see the head motion, and it happens several times.

Lawyers kind of bothering him, not quite shaking him, but certainly trying to get his attention. And that head snapping motion, we felt confident enough to report that Trump fell asleep.

During his own criminal trial’s opening day.

Does someone eventually wake him up?

He wakes up. He wakes up. And in fact, in the afternoon, he’s much more animated. It’s almost as if he wants to be seen being very much awake.

Right. So once these pre-trial motions are ruled on and Trump is snapped back to attention, what happens?

Well, what happens in the courtroom is that the trial begins. The first trial of an American president is now in session. And what marks that beginning is jurors walking into the room one by one — many of them kind of craning their necks over at Donald Trump, giggling, raising their eyebrows at each other, filing into the room, and being sworn in by the judge. And that swearing in marks the official beginning of the trial.

The beginning is jury selection, and it’s often overlooked. It’s not dramatized in our kind of courtroom dramas in the same way. But it’s so important. It’s one of the most important parts of the case. Because whoever sits on the jury, these are the 12 people who are going to decide whether Trump is guilty or whether Trump is innocent.

So how does jury selection actually look and feel and go?

So, jury selection is a winnowing process. And in order to do that, you have to have these people go through a bunch of different hurdles. So the first hurdle is, after the judge describes the case, he asks the group — and there are just short of 100 of them — whether they can be fair and impartial. And says that if they can’t, they should leave. And more than half the group is instantly gone.

So after we do this big mass excusal, we’re left with the smaller group. And so now, jurors are getting called in smaller groups to the jury box. And what they’re going to do there is they’re going to answer this questionnaire.

And this part of the process is really conducted by the judge. The lawyers are involved. They’re listening, but they’re not yet asking questions of the jurors themselves.

And what’s on the questionnaire?

Well, it’s 42 questions. And the questions include, their education, their professional histories, their hobbies, what they like to do whether you’re a member of QAnon or Antifa.

Whether you’re far left or far right.

That’s right. Whether you’ve read “The Art of the Deal,” Trump’s book, which some prospective jurors had.

Right. It was a bestseller in its time.

That’s right. And some of it can be answered in yes/no questions, but some of it can be answered more at length. So some of the prospective jurors are going very, very fast. Yes, no, no, no, yes.

Right. Because this is an oral questionnaire.

That’s right. But some of them are taking their time. They’re expanding on their hobbies. So the potential juror in seat 3, for example, is talking about her hobbies. And she says some running, hiking. And then she said, I like to go to the club, and it got a huge laugh. And you get that kind of thing in jury selection, which is one of the reasons it’s so fun. It’s the height of normality in this situation that is anything but normal.

Right. The most banal answer possible delivered in front of the former president And current Republican nominee for president.

Well, that’s one of the fascinating parts about all this, right? is that they’re answering in front of Trump. And they’re answering questions about Trump in front of Trump. He doesn’t react all that much. But whenever someone says they’ve read “The Art of the Deal —” and there are a few of those — he kind of nods appreciatively, smiles. He likes that. It’s very clear. But because there are so many questions, this is taking forever, especially when people are choosing to answer and elaborate and digress.

This is when you fall asleep.

This Is. When I would have fallen asleep if I were a normal person.

And by the end of the day. Where does jury selection stand?

Well, the questionnaire is another device for shrinking that jury pool. And so the questionnaire has almost these little obstacles or roadblocks, including, in fact, a question that jurors have seen before — whether they would have any problem being fair and impartial?

Hmm. And they ask it again.

They’re asked it again. And they’re asked in this more individualized way. The judge is questioning them. They’re responding.

So, remember that woman who said she liked to go to the club got a big laugh. She reaches question 34. And question 34 reads, “Do you have any strong opinions or firmly-held beliefs about former President Donald Trump or the fact that he is a current candidate for president that would interfere with your ability to be a fair and impartial juror?” She said, yes, she does have an opinion that would prevent her from being fair and impartial. And she, too, is excused.

So that’s how it works. People answer the questionnaire, and they get excused in that way, or they have a scheduling conflict once they reach the jury box. And so to answer your question, Michael. At the end of day one, given all these problems with the questionnaire and the length of time it’s taken to respond to and people getting dismissed based on their answers, there is not a single juror seated for this trial.

And it’s starting to look like this is going to be a really hard case for which to find an impartial jury.

That’s the feeling in the room, yeah.

We’ll be right back.

So Jonah, let’s turn to day 2. What does jury selection look like on Tuesday?

So when the day begins, it looks almost exactly like it looked when the day ended on Monday. We’re still with the questionnaire, getting some interesting answers. But even though it feels like we’re going slow, we are going.

And so we’ve gone from about 100 people to now there’s about 24 the room there’s 18 the jury box. And by the time we hit lunch, all those people have answered all those questions, and we are ready for the next step in the process.

Voir dire. And what it is the heart of jury selection. This is the point where the lawyers themselves finally get to interview the jurors. And we get so much information from this moment because the lawyers ask questions based on what they want out of the jurors.

So the prosecution is asking all these different kinds of questions. The first round of wajir is done by a guy named Joshua Steinglass, a very experienced trial lawyer with the Manhattan District Attorney’s Office. And he’s providing all these hypotheticals. I’ll give you one example because I found this one really, really interesting. He provides a hypothetical about a man who wants his wife killed and essentially hires a hitman to do it. And what he asked the jurors is, if that case were before you, would you be able to see that the man who hired the hitman was a part of this crime?

And of course, what he’s really getting at is, can you accept that even though Michael Cohen, Trump’s fixer, made this payment, Trump is the guy who hired him to do it?

That’s right. If there are other people involved, will jurors still be able to see Donald Trump’s hands behind it all?

Fascinating. And what were some of the responses?

People mostly said, yes, we accept that. So that’s how the prosecution did it.

But the defense had a totally different method of voir dire. They were very focused on their client and people’s opinions about their client.

So what kind of questions do we get from them?

So the lawyer, Todd Blanche, is asking people, what do you make of President Trump? What do you think of President Trump?

And what are some of the responses to that?

Well, there’s this incredible exchange with one of the jurors who absolutely refuses to give his opinion of Donald Trump. They go back and forth and back and forth. And the juror keeps insisting you don’t need to know my opinion of him. All you need to know is that I’m going to be fair and impartial, like I said. And Blanch pushes, and the guy pushes back. And the only way the guy budges is he finally kind of confesses almost at the end that, yes, I am a Democrat, and that’s all we get.

And what ends up happening to this potential juror?

Believe it or not, he got dismissed.

[LAUGHS]: I can believe it. And of course, it’s worth saying that this guy and everybody else is being asked that question just feet from Trump himself.

That’s right. And you might think you were going to get a really kind of spicy, like, popcorn emoji-type exchange from that. But because these are now jurors who have said they can be fair and impartial, who, to some extent, want to be on this jury or at least wouldn’t mind being on this jury, they’re being very restrained.

Mostly, what they are emphasizing — much like that guy just described dis — is that they can be fair. They can be impartial. There’s one woman who gives this really remarkable answer.

She says, I thought about this last night. I stayed up all night. I couldn’t sleep, thinking about whether I could be fair. It’s really important to me, and I can.

What ends up happening to that particular juror?

She’s also dismissed. And she’s dismissed without any reason at all. The defense decides it doesn’t like her. It doesn’t want her on the jury. And they have a certain number of chances to just get rid of jurors — no questions asked.

Other jurors are getting dismissed for cause — I’m doing air quotes with my hands — which means that the lawyers have argued they actually revealed themselves through their answers or through old social media posts, which are brought up in the courtroom, to be either non-credible, meaning they’ve said they can be fair and they can’t, or somehow too biased to be on the jury.

Wait, can I just dial into that for a second? Are lawyers researching the jurors in real time going online and saying — I’m making this up — but Jonah Bromwich is a potential juror, and I’m going to go off into my little corner of the courtroom and Google everything you’ve ever said? Is that what’s happening in the room?

Yeah, there’s a whole profession dedicated to that. It’s called jury consultant, and they’re very good at finding information on people in a hurry. And it certainly looked as if they were in play.

Did a social media post end up getting anybody kicked off this jury?

Yes, there were posts from 2016 era internet. You’ll remember that time as a very heated one on the internet, Facebook memes are a big thing. And so there’s all kinds of lock him up type memes and rhetoric. And some of the potential jurors here have used those. And those jurors are dismissed for a reason.

So we have these two types of dismissals, right? We have these peremptory dismissals — no reason at all given. And we have for cause dismissals.

And the process is called jury selection. But you don’t actually get selected for a jury. The thing is to make it through all these obstacles.

You’re left over.

Right. And so when certain jurors are not dismissed, and they’ve made it through all these stages, by the end of the day, we have gone from zero juror seated to seven jurors who will be participating in Donald Trump’s trial.

Got it. And without going through all seven, just give us a little bit of a sketch of who so far is on this jury. What stands out?

Well, not that much stands out. So we’ve got four men. We’ve got three women. One lives on the Upper East Side. One lives in Chelsea. Obviously, they’re from all over Manhattan.

They have these kind of very normal hobbies like spending time with family and friends. They have somewhat anonymous jobs. We’ve got two lawyers. We’ve got someone who’s worked in sales.

So there’s not that much identifying information. And that’s not an accident . One of the things that often happens with jury selection, whether it be for Donald Trump or for anyone else, is the most interesting jurors — the jurors that kind of catch your attention during the process — they get picked off because they are being so interesting that they interest one or the other side in a negative way. And soon they’re excused. So most of the jurors who are actually seated —

Are not memorable.

Are not that memorable, save one particular juror.

OK. All right, I’ll bite. What do I need to know about that one particular juror?

So let me tell you about a prospective juror who we knew as 374, who will now be juror number five. She’s a middle school teacher from Harlem. And she said that she has friends who have really strong opinions about Trump, but she herself does not. And she insisted several times, I am not a political person.

And then she said this thing that made me quite surprised that the prosecution was fine with having her on the jury. She said, quote, “President Trump speaks his mind, and I’d rather that than someone who’s in office who you don’t know what they’re thinking.”

Hmm. So she expressed approval of President Trump.

Yeah, it was mild approval. But the thing is, especially for the defense in this trial, all you need is one juror. One juror can tie up deliberations in knots, and you can end with a hung jury. And this is actually something that I saw firsthand. In 2019, I was the foreperson on a jury.

How you like that?

Yeah. And the trial was really complicated, but I had thought while we were doing the trial, oh, this is going to be a really easy decision. I thought the defendant in that case was guilty. So we get into deliberations, but there’s this one juror who keeps gumming up the works every time we seem to be making progress, getting a conversation started.

This juror proverbially throws up his hands and says, I am not convicting. This man is innocent. And we talked and we talked. And as the foreperson, I was trying to use all my skills to mediate.

But any time we made any progress, this guy would blow it up. And long story short, hung jury — big victory for the defense lawyer. And we come out of the room. And she points at this juror. The guy —

The defense lawyer.

The defense lawyer points at this juror who blew everything up. And she said, I knew it. I knew I had my guy.

OK. I don’t want to read too much into what you said about that one juror. But should I read between the lines to think that if there’s a hung jury, you wonder if it might be that juror?

That’s what everyone in the courtroom is wondering not just about this juror, but about every single person who was selected. Is this the person who swings the case for me? Is this the person who swings the case against me?

These juries are so complex. It’s 12 people who don’t know each other at the start of the trial and, by the end of the trial, have seen each other every morning and are experiencing the same things, but are not allowed to have talked about the case until deliberations start. In that moment when deliberations start —

You’re going to learn a whole lot about each other.

That’s right. There’s this alchemical moment where suddenly, it all matters. Every personality selected matters. And that’s why jury selection is so important. And that’s why these last two days are actually one of the most important parts of this trial.

OK. So by my math, this trial will require five more jurors to get to 12. I know also they’re going to need to be alternates. But from what you’re saying what looked like a really uphill battle to get an impartial jury or a jury that said it could be impartial — and Trump was very doubtful one could be found — has turned out to not be so hard to find.

That’s right. And in fact, we went from thinking, oh, boy, this is going awfully slowly, to the judge himself saying we could be doing opening arguments as soon as Monday morning. And I think that highlights something that’s really fascinating both about this trial and about the jury selection process overall.

One of the things that lawyers have been arguing about is whether or not it’s important to figure out what jurors’ opinions about Donald Trump are. And the prosecution and, I think, the judge have really said, no, that’s not the key issue here. The key issue is not whether or not people have opinions about Donald Trump.

Right. Who doesn’t have an opinion about Donald Trump?

Exactly. They’re going to. Automatically, they’re going to. The question is whether or not they can be fair and impartial. And the seven people we already have seated, and presumably the five people that we’re going to get over the next few days and however many alternates — we expect six — are all going to have answered that question, not I hate Trump; I love Trump, but I can weigh in on the former president’s innocence or guilt, and I can do it as fairly as humanly possible.

Now, Trump is not happy about this. He said after court yesterday, quote, We have a highly conflicted judge, and he’s rushing this trial.” And I think that he is going to see these beats of the system the criminal justice system as it works on him as he is experiencing it as unfair. That is typically how he talks about it and how he views it.

But what he’s getting is what defendants get. This is the system in New York, in the United States. This is its answer to how do you pick a fair jury? Well, you ask people can you be fair? And you put them through this process, and the outcome is 12 people.

And so I think we’re going to see this over and over again in this trial. We’re going to see Trump experience the criminal justice system.

And its routines.

Yeah, openings, witnesses, evidence, closings. He’s going to go through all of it. And I think, at every turn, it makes sense to expect him to say, well, this is not fair. Well, the judge is doing something wrong. Well, the prosecutors are doing something wrong. Well, the jury is doing something wrong.

But at the end of the day, he’s going to be a defendant, and he’s going to sit, mostly silently if his lawyers can make him do that, and watch this process play itself out. So the system is going to try and treat him like any other defendant, even though, of course —

— he’s not. And he is going to fight back like no other defendant would, like no other defendant could. And that tension, him pushing against the criminal justice system as it strives to treat him, as it would anyone else, is going to be a defining quality of this trial.

Well, Jonah, thank you very much. We appreciate it.

Of course. Thanks so much for having me. [MUSIC PLAYING]

PS, have you ever fallen asleep in a trial?

I have not.

[CHUCKLES]:

Here’s what else you need to know today.

It’s clear the Israelis are making a decision to act. We hope they do so in a way that does as little to escalate this as possible and in a way that, as I said —

During a visit to Jerusalem on Wednesday, Britain’s foreign Secretary left little doubt that Israel would retaliate against Iran for last weekend’s aerial attack, despite pressure from the United States and Britain to stand down. The question now is what form that retaliation will take? “The Times” reports that Israel is weighing several options, including a direct strike on Iran, a cyber attack, or targeted assassinations. And —

Look, history judges us for what we do. This is a critical time right now, critical time on the world stage.

In a plan that could threaten his job, Republican House Speaker Mike Johnson will put a series of foreign aid bills up for a vote this weekend. The bills, especially for aid to Ukraine, are strongly opposed by far-right House Republicans, at least two of whom have threatened to try to oust Johnson over the plan.

I can make a selfish decision and do something that’s different, but I’m doing here what I believe to be the right thing. I think providing lethal aid to Ukraine right now is critically important. I really do. I really — [MUSIC PLAYING]

Today’s episode was produced by Rikki Novetsky, Will Reid, Lynsea Garrison, and Rob Zubko. It was edited by Paige Cowett, contains original music by Marion Lozano, Elisheba Ittoop, and Dan Powell, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly Lake.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

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Hosted by Michael Barbaro

Featuring Jonah E. Bromwich

Produced by Rikki Novetsky ,  Will Reid ,  Lynsea Garrison and Rob Szypko

Edited by Paige Cowett

Original music by Dan Powell ,  Marion Lozano and Elisheba Ittoop

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Political and legal history are being made in a Lower Manhattan courtroom as Donald J. Trump becomes the first former U.S. president to undergo a criminal trial.

Jonah Bromwich, who covers criminal justice in New York, explains what happened during the opening days of the trial, which is tied to Mr. Trump’s role in a hush-money payment to a porn star.

On today’s episode

problem solving about percent

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

Former president Donald Trump sitting in a courtroom.

Background reading

Here’s a recap of the courtroom proceedings so far.

Mr. Trump’s trial enters its third day with seven jurors chosen.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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IMAGES

  1. Solving Percent Problems (examples, solutions, worksheets, videos

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  2. Solving Percent Problems Worksheet Pdf

    problem solving about percent

  3. Solving Percentage Word Problems

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  4. Solving Percent Problems from Math Through Discovery LLC

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  5. Solving Percentage Word Problems

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  6. Solving Percent Problems Worksheet Pdf

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VIDEO

  1. Percent Trick...in Seconds

  2. Solving a Percent Problem by Translating Words into an Equation

  3. Solving a Percent Problem by Translating Words into an Equation

  4. PERCENTS TRICK 🤯

  5. Solving a Percent Problem by Translating Words into an Equation

  6. Technical Mathematics Section 4.4: Solving for Percent in Percent Problem

COMMENTS

  1. 5.2.1: Solving Percent Problems

    Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as n 100 n 100. The other ratio is the amount to the base. Percent = amount base Percent = amount base.

  2. How to Solve Percent Problems? (+FREE Worksheet!)

    How to Solve Simple Interest Problems; Step by step guide to solve percent problems . In each percent problem, we are looking for the base, or part or the percent. Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base

  3. How to Solve Percent Problems

    So, to find 35% of 80, you would rewrite it as: 35% of 80 = 0.35 80. Solve the problem using decimal multiplication. Here's what the example looks like: So 35% of 80 is 28. As another example, suppose you want to find 12% of 31. Again, start by changing the percent to a decimal and the word of to a multiplication sign:

  4. 4.2: Percents Problems and Applications of Percent

    Solving Percent Problems: Percent Increase. When a quantity changes, it is often useful to know by what percent it changed. If the price of a candy bar is increased by \(50\) cents, you might be annoyed because it's it's a relatively large percentage of the original price. If the price of a car is increased by \(50\) cents, though, you ...

  5. Percentages

    Math; Pre-algebra; Unit 4: Percentages. 700 possible mastery points. Mastered. Proficient. Familiar. Attempted. Not started. Quiz. Unit test. ... Percent word problems Get 5 of 7 questions to level up! Quiz 3. Level up on the above skills and collect up to 160 Mastery points Start quiz. Up next for you:

  6. Solving percent problems (video)

    25% is part of a whole 100%.*. *25% is 1/4 of 100%*. so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the ...

  7. Percentages

    Convert the quotient to a percentage. % change = final − initial initial × 100. To calculate the percent change, the initial value, or the final value given the other two, we: Write an equation that relates the initial and final values using a percentage. Plug in the known values. Solve for the unknown quantity.

  8. Solving Percent Problems (solutions, examples, worksheets, videos

    Lesson 29 Summary. • Percent problems have three parts: whole, part, percent. • Percentage problems can be solved using models such as ratio tables, tape diagrams, double number line diagrams, and 10 x 10 rids. Claim: To find 10% of a number all you need to do is move the decimal to the left once. Use at least one model to solve each ...

  9. Solving problems with percentages (Pre-Algebra, Ratios and percent

    To solve problems with percent we use the percent proportion shown in "Proportions and percent". a b = x 100 a b = x 100. a b ⋅b = x 100 ⋅ b a b ⋅ b = x 100 ⋅ b. a = x 100 ⋅ b a = x 100 ⋅ b. x/100 is called the rate. a = r ⋅ b ⇒ Percent = Rate ⋅ Base a = r ⋅ b ⇒ P e r c e n t = R a t e ⋅ B a s e. Where the base is the ...

  10. Solving Percent Problems (examples, solutions, worksheets, videos

    Examples, solutions, and videos that will help GMAT students review how to solve percent word problems. The following diagram shows some examples of solving percent problems using the part, base, rate formula. Scroll down the page for more examples and solutions of solving percent problems. Solving Percent Problems. Show Step-by-step Solutions.

  11. How to Solve Percent Problems? (13 Amazing Examples!)

    How to Solve Percent Problems? 13 Amazing Examples! Ratios and proportions help us in solving problems with percents. Why? Because a percent is the ratio (fraction) of one number to another. In other words, its a number divided by 100. What is most important to note is that our overall goal is to translate each problem into an algebraic ...

  12. Solving Percent Problems

    Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100.. You can then use cross multiplication to ...

  13. Percent Maths Problems

    Problem 6. A number increases from 30 to 40 and then decreases from 40 to 30. Compare the percent of increase from 30 to 40 and that of the decrease from 40 to 30. Solution to Problem 6. Percent increase from 30 to 40 is given by. (40 - 30) / 30 = 10 / 30 = 0.33 = 33% (2 significant digits) Percent decrease from 40 to 30 is given by.

  14. Solving percent problems

    Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fr...

  15. Math: Basic Tutorials : Solving Percent Application Problems

    Solving Percent Application Problems Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem.

  16. Percent problems (practice)

    Percent problems. A brand of cereal had 1.2 milligrams ( mg) of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving. What was the percent increase in iron? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.

  17. Art of Problem Solving

    Percent of a Number. Let be the percentage, be the number we want to take the percentage of, and be the wanted quantity. By definition, , so . In other words, to find the percent of the number, we convert the percent to the fraction (or decimal) and then multiply it with the number we want to take the percentage of. For example, of equals .

  18. PDF Percent Equation P B A

    Percent Proportion. Problems involving the percent equation can also be solved with the proportion: Percent Amount (is) =. 100 Base (of) When the percent is given, drop the percent sign and place the percent over 100. Cross multiply to solve the proportion. Example 2: 27 is 45% of what number?

  19. Solving Percent Problems

    The percent has the percent symbol (%) or the word "percent." In the problem above, 15 % is the percent off the purchase price. The base is the whole amount. In the problem above, the whole price of the guitar is $ 220, which is the base. The amount is the number that relates to the percent. It is always part of the whole.

  20. Different Types of Percentage Problems

    Now we will apply the concept of percentage to solve various real-life examples on percentage. Solved examples on percentage: 1. In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.

  21. Solving Percent Problems

    Percent is a great mathematical tool to express quantities and is used extensively in different things - from interest rates, discounts, and taxes to surveys, censuses, etc.. This article is your guide to percent and solving percent problems frequently appearing in major national examinations.

  22. The 5 Percent Problem

    The percentage of students using the other products as prescribed is similarly low. Imagine a doctor prescribing a sophisticated new drug to 100 patients and finding 95 of them didn't take it as prescribed. That is the situation with many online math interventions in K-12 education today. They are a solution for the 5 percent.

  23. The Opening Days of Trump's First Criminal Trial

    12. Hosted by Michael Barbaro. Featuring Jonah E. Bromwich. Produced by Rikki Novetsky , Will Reid , Lynsea Garrison and Rob Szypko. Edited by Paige Cowett. Original music by Dan Powell , Marion ...