PROPORTION PROBLEMS

PERCENTS

Concept: A ratio is a comparison of two numbers. It can be written in several ways. For example, when comparing the numbers 1 and 2, we can express the comparison as 1 to 2, or 1 : 2 or ½.

Always write the terms of the ratio in the same order as the problem compares them.

Just as we can reduce fractions to lowest terms, we can simplify ratios to their lowest terms, although a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.

Many ratio problems require more than one step.

You may not be given both of the numbers that you need to write a ratio. In this case, you may need to solve another equation to find the missing number.

Finally, when two ratios are written as equal ratios, the equation is called a proportion. For example, is a proportion. In many proportion problems, one of the four terms is missing.

The proportion can be solved using the Cross-product Rule.

Cross-product Rule
To find the missing number in a proportion, cross multiply, and divide the product by the third number. For example, in the proportion , first multiply . Then divide . In this problem .

Steps for Solving Simple Proportion Problems

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.

Example 1: 30 of 100 is the same as what number of 73?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 21.9
30 of 100 is the same as what number of 73? 21.9

Example 2: 79 percent is the same as how many per 100?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 79
79 percent is the same as 79 per 100.

Example 3: 69 percent is the same as what number of 4?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 2.76
69 percent is the same as what number of 4? 2.76

Example 4: 40 percent is the same as what number of 83?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 33.2.
40 percent is the same as what number of 83? 33.2

Example 5: How many of 29 do you have if you have 46 per 100 of them?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 13.34
How many of 29 do you have if you have 46 per 100 of them? 13.34

Example 6: 22 percent is the same as what number of 20?

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 4.4.
22 percent is the same as what number of 20? 4.4