# Basics of percent - a free lesson

Learn the basics of the concept of percent in this easy lesson! Percent (or per cent) means one hundredth. Therefore, 1% means 1/100 or one hundredth, and 7% means 7/100 or seven hundredths. Since percentages are just hundredth parts (which means they are FRACTIONS), we can very easily write them as fractions and as decimals.

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

 Percent (or per cent) means one hundredth. The symbol for percent is  %. Therefore, 1% means 1/100 or one hundredth, and 7% means 7/100 or seven hundredths. The words “per cent” actually mean “per hundred” in Latin.
Since percentages are just hundredth parts, we can very easily write them as fractions and as decimals.

 63%  = 63 100 =  0.63
 9%  = 9 100 =  0.09

1. Write the shaded part and the unshaded part as fractions, as decimals, and as percentages.

a.

 =  _____ = _____%

 =  _____ = _____%
b.

 =  _____ = _____%

 =  _____ = _____%

2. Write as percentages, fractions, and decimals.

 a. 28%  = 28 100 =  0.28
 b. 17%  = =  _____

3. Typically seven out of every 100 babies born in the River Creek hospital have a birth
defect, most of them minor defects.

a. What typical percentage of the babies have birth defects?

b. What typical percentage of the babies do not have birth defects?

c. About how many babies with birth defects would you expect to find
in a group of 500 babies?

Other fractions as percents

What part of the pencils are short?

Two out of five, or 2/5 of them are short.

Let’s rewrite 2/5 with a denominator of 100
using the method for equivalent fractions:

 × 20 2 5 = 40 100 × 20
Now we can write 40/100 as 40%.
So 40% of the pencils are short.

4. Write what part of the pencils are short, both as a fraction and as a percentage.
Use equivalent fractions.

 a. = 100 =  ____%

 b. = 100 =  ____%

5. Convert the fractions into equivalent fractions with denominator 100, and write
them as percentages.

 a. 4 10 = 100 =  _____%
 b. 11 20 = 100 =  _____%

6. Write what part of the rectangle is shaded and what part is unshaded,
both as fractions and percentages.

a.

b

 Percentages that are more than 100% The image shows 1 whole and 55/100. As a mixed number, we write 1 55/100. As a decimal, we write 1.55. Since 55/100 is 55%, and one whole is 100%, the image shows 155%.
So we can use percentages that are more than 100%. Just remember that 100% is 1, and 1% is 0.01.

 200%  = 200 100 = 2
 308%  = 308 100 =  3.08

7. Write as fractions, decimals, and percentages.

 a. 100 =  _____ = _____%

 b. 100 =  _____ = _____%

8. Write as percentages, fractions, and decimals.

 a. 105%  = =   ______
 b. 457%  = =  ______

9. Write the fractions as percentages.

a. About 4/5 ( _______ %) of the United States population is 14 years old or older.

b. About 2/25 ( _______ %)  of the world’s population lives in North America.

c. The continent of Africa covers about 1/5 ( _______ %) of the Earth’s total land mass.

10. Two trees are growing in Sandy’s front yard. The taller one is 5/4 as tall
as the shorter one.

a. Write the second sentence using a percent instead of a fraction.

b. If the shorter tree is 160 cm tall, how tall is the taller tree?

Change any fraction to a percentage

To write 1/7 as a percentage, you can either:

• Divide 1 by 7 using long division or a calculator. You will get
a decimal number. Express that as a percentage. OR,
• Find 1/7 of 100%; in other words divide 100 by 7.

Dividing 100 by 7, we get 14.28...
Rounded to the nearest whole percent, that is 14%.

How many percent would 2/7 be?

 0 1 4 . 2 8 7 ) 1 0 0 . 0 0 7 3 0 - 2 8 2 0 - 1 4 6 0 - 5 6 4

11. Write the fractions as percentages. Use long division. Round your

 a. =  ______%

 b. =  ______%

12. Write the fractions as percentages. Round the answers to
the nearest percent.

a. About 1/20 ( _________ %) of the population of India is 65 years old or older.
(2009 estimate)

b. About 13/100 ( ________ %) of the population of Australia is 65 years old or older
(2009 estimate)

13. Write as a percentage. Round your answers to the nearest percent.

a. 8/7

b. 1 3/8

 How many percent of this figure is colored?

Percentage of a number using mental math – free lesson

How to calculate percentages of numbers – free lesson

How to calculate percentages – free lesson

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.