# How to calculate percentages

Learn how to calculate percentages in this easy lesson! When you're asked to calculate an (unknown) percentage ("What percentage...?"), you need to first write the fraction PART/TOTAL, and then simply write that fraction as a decimal and as a percentage. See many examples below.

The concepts and ideas of this lesson are also explained in this video:

 What percentage of the height of a 15-ft tree is a 3-ft sapling? A choir has 22 women and 18 men. Find what percentage of the choir’s members are men. One pair of jeans costs \$25 and another costs \$28. How many percent is the price of cheaper jeans of the price of the more expensive jeans?

Look carefully at the questions above. Notice that the problems don’t tell you the percentage; in other words, there is no number in the problem written as x%. Instead, they ask you to find it!

 Questions with  “What percentage ... ?” or "How many percent ... ?" Asking “What percentage?” or "How many percent?" is the same as asking “How many hundredth parts?” We can solve these questions in a two-part process: First find out the part that is being asked for as a fraction. The denominator probably won’t be 100. Convert that fraction to a decimal. Then you can easily convert the decimal to a percentage! Example 1. A choir has 22 women and 18 men. Find what percentage of the choir’s members are men. Find out what part (fraction) of the choir’s members are men. That is 18/40, or 9/20. Write 9/20 as a percent. Use equivalent fractions: 9/20 = 45/100 = 45%. Example 2. One pair of jeans costs \$25 and the other costs \$28. How many percent is the price of cheaper jeans of the price of the more expensive jeans? Write what part the cheaper price is of the more expensive price. The answer is 25/28. Write 25/28 as a percentage. A calculator gives 25/28 = 0.8928...   Rounded to the nearest whole percent, that’s 89%.

1. a. What percentage of a 15-ft tree is a little 3-ft sapling?

b. How many percent is \$12 of \$16?

2. Find how many percent the smaller object’s height is of the taller object’s height. 6 m 8 m

a. 300 cm 120 cm

b.

3. A 2-year old child measures 32 inches tall and weighs 24 pounds. A 10-year old child measures 52 inches tall and weighs 96 pounds.

a. How many percent is the smaller child’s age of the older child’s age?

b. How many percent is the smaller child’s height of the older child’s height?

4. Write the percentages into the sectors in the circle graphs Think of fractions!  5. The circle graph at the right gives the angle measure of each sector of the circle. Find what percentage each sector is of the whole circle, and write the percentage in the sector. Remember, the whole circle is 360°.

Percent – free lesson

Percentage of a number using mental math – free lesson

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Basics of percent of change – free lesson

Interactive fraction, decimal and percentage tool
This tool shows you a fraction visually (bar or pie) and converts the fraction into a percentage and decimal. You can show or hide the equivalent percentage and decimal.
/interactives/fraction_decimal_percentage.php

This lesson is taken from Maria Miller's book Math Mammoth Percent, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.