Workplace Math and PLAR Prep

Percent, Ratio and Proportion

Percent

Percent is another way to describe a part or fraction of something.

The only denominator that a percent can have is 100.

This denominator is shown by a percent sign %.

The word percent and the sign % both mean hundredths.

For example: 25% is the same as 25/100 or 1/4 or .25

Although percent means out of one hundred, a percent can be more than 100. A percent larger than 100 is equal to an improper fraction. When working with percent problems, you need to change the percent to a decimal or fraction.

Changing Percents to Decimals

Here is how to change 85% to a decimal:

1. Drop the percent sign. 85

2. In a number with no decimal point, it is understood that the decimal point is at the end of the number. Put in the decimal point: 85.

3. Now that you have a decimal point, move it two places to the left. 0.85 = 85% = .85 = 85 hundredths

The tricky part is putting in the decimal point.

Study these examples:

5 % = .05
10% = .10
55% = .55
3% = .03

For example:

Change 25 1/4 % to a decimal.

1. Drop the percent. 25 1/4

2. Change 1/4 to a decimal. 4 ÷ 1= .25

3. Put in the decimal point. 25.25

4. Move the decimal point 0.2525

Changing Decimals to Percents

You just learned how to change a percent to a decimal by moving the decimal point two places to the left. Changing a decimal to a percent is just the opposite.

For example: Change 0.43 to a percent.

1. Move the decimal point 0.43 two places to the right.

2. The decimal point is at the 43 end of the number where it can be dropped.

3. Add the percent. 43%

Try this one: Change 0.217 to a percent. Then click the arrow to see the answer ---->

1. Move the decimal point 21.7 two places to the right.

2. The decimal point is not at the 21.7 end of the number so you cannot drop it.

3. Add the percent. 21.7%

Changing Percents to Fractions

Now that you can change a percent to a decimal, you can change a percent to a fraction because you can use that as the first step in this example.

For example: Change 15% to a fraction.

1. Change the percent to a decimal. 0.15

2. Now change the decimal 0.15 = to a fraction. 0.15 = 15/100

3. Reduce the fraction. 15/100 = 3/20

Finding a Percent of a Number

Percents are very common in the everyday world. Learning how to solve percent problems will be helpful in figuring out discounts on items you buy or figuring interest on loans. There are different methods for finding a percent of a number.

For example: Find 10% of 150.

1. Change the percent to a decimal. 10% = 0.10

2. Multiply. 0.10 x 150 = 15

3. 10% of 150 is 15.

Let’s try this one: Find 7% of 40. Then click the arrow to see your answer ----->

1. Change the percent to a decimal. 7% = 0.07

2. Multiply. 0.07 x 40 = 2.8

3. 7% of 40 is: 2.8

Finding what percent one number is of another is a similar problem that can be solved by writing the problem as a proportion. (more about proportions below)

Notice the difference in the way this problem is written as a proportion.

Follow this example: What percent of 45 is 9? 1.

Write the unknown percent as a fraction, using x to stand for the unknown. X% = x/100.

2. Use the fraction to write the problem as a proportion

3. Cross multiply. x x 45 = 100 x 9

45x = 900

45x /45 = 900/45

x = 20

4. 9 is 20% of 45

Let’s try this one: 48 is 16% of what number? (then check your answer below)

1. Write the percent as a fraction. 16% =16/100.

2. Use the fraction to write the problem as a proportion. 16/100 = 48/x

3. Cross multiply 16x = 4800

x = 4800/16

x = 300

4. 48 is 16% of 300.

Ratio

A ratio is a comparison of one number with another. It is used to show the relationship between something and something else.

The order of the numbers in a ratio is important. When you write a ratio, you must keep in mind which number belongs to which thing. A ratio can be written three ways:

1. With the word “to” 3 to 5

2. With a colon 3:5

3. As a fraction 3/5

Remember: When ratios are written as fractions, they are usually reduced to their lowest terms, even improper fractions, but you should not change an improper fraction to a whole number or a mixed number.

For example: Suppose you come into a room and see that there are 15 people but only 10 chairs.

The ratio of people to chairs is:

15 to 10 ÷ 5/5 = 3 to 2
15 : 10 ÷ 5/5= 3 : 2
15/10 divided 5/5 = 3/2

The ratio of chairs to people is 10 to 15 or 2 to 3.

Proportions

A proportion is a statement that two ratios are equal.

This is how it is shown:

15/10 = 3/2 or 15:10 = 3:2

It is read: “ fifteen is to ten as three is to two”.

If proportions are equal, cross-multiply and the answer should be the same. 15 x 2 = 10 x 3

Cross-multiplication can be used to find an unknown number in a proportion.

For example: 5 is to 10 as 20 is to an unknown number.

1. Write the proportion, letting “a” stand for the unknown number.

2. Cross-multiply. 5 X a = 10 x 20

5a = 200

a = 200 ÷ 5

a = 40

For practice, see the worksheets below:

Math #6 Ratio, Proportion and Percent.pdf

Go here for worksheets

www.math-drills.com/percentsworksheets.php

Next: Simple and Compound Interest

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