Applying Percents Study Guide

What is a Percent?

A percent is a way of expressing a number as a fraction of 100. The symbol "%" is used to denote a percent. For example, 25% means 25 out of 100.

Converting Between Percents, Decimals, and Fractions

To convert a percent to a decimal, divide the percent by 100. For example, 25% is equivalent to 0.25 as a decimal.

To convert a percent to a fraction, write the percent as a fraction with a denominator of 100 and simplify if possible. For example, 25% is equivalent to 25/100, which simplifies to 1/4.

To convert a decimal to a percent, multiply the decimal by 100. For example, 0.25 is equivalent to 25% as a percent.

To convert a decimal to a fraction, write the decimal as a fraction and simplify if possible. For example, 0.25 is equivalent to 25/100, which simplifies to 1/4.

Calculating Percentages

To calculate a percentage of a number, multiply the number by the decimal equivalent of the percentage. For example, to find 25% of 80, you would calculate 0.25 * 80 = 20.

Percent Increase and Decrease

To calculate a percent increase, first find the difference between the new and original values. Then, divide the difference by the original value and multiply by 100. For example, if the original value is 50 and the new value is 65, the percent increase is ((65-50)/50) * 100 = 30%.

To calculate a percent decrease, use the same process as for percent increase, but with the difference being the original value minus the new value.

Discounts and Markups

To calculate the sale price of an item after a discount, subtract the discount amount from the original price. For example, if an item is originally $80 and there is a 20% discount, the sale price would be $80 - (0.20 * $80) = $64.

To calculate the selling price of an item after a markup, add the markup amount to the original price. For example, if an item is originally $50 and there is a 25% markup, the selling price would be $50 + (0.25 * $50) = $62.50.

Word Problems

When solving percent word problems, it's important to carefully read the problem and identify the known values and the unknown value. Then, set up an equation and solve for the unknown value using the methods described above.

Practice Problems

What is 30% as a decimal?
Convert 0.6 to a percent.
Find 15% of 200.
If the original price of a shirt is $40 and it is discounted by 20%, what is the sale price?
If a computer is marked up by 35% to a selling price of $810, what was its original price?

Good luck with your study of applying percents!

◂Math Worksheets and Study Guides Seventh Grade. Applying Percents

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).