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Chapter 6—Expressions and Equations 68 Ratio and Proportion
A First Look at Ratios and Proportions
Example There are 14 guys and 20 girls in the class.
Examples & Exercises
In a proportion such as , a does not necessarily equal c, nor does b necessarily equal d. The ratios, however, are equal. Consider this simple numerical example: ^{ 3}/_{4} = ^{6}/_{8}. The 3 does not equal 6, nor does the 4 equal 8. If you do the division for the two ratios, however, you see that 0.75 = 0.75. That's obviously true. Also, if you crossmultiply, you will find the terms are equal. CrossMultiplying Proportions One of the most important and useful characteristics of proportions is the process of cross multiplying. You can almost say that every time you use proportions, you will be doing a crossmultiplication on some level.
Examples
Examples & Exercises
Proportions are not always expressed with values that happen to be positive integers. Some of the terms may be negative, and some may be decimal fractions. See the following examples. Examples:
Examples & Exercises
Solving Proportions Here is an example of a proportion that includes an unknown value:. This is saying: x is to 12 and 1 is to 4. What is the value of x? You can probably guess the value of x is 3. But it's important you understand a formal procedure for solving proportions like this. Step 1. Cross multiply the ratios.
Step 2. Divide both sides of the equal sign by 4, and simplify. If x truly equals 3 in this proportion, then you should be able to substitute 3 for x in the original problem, and see if the result is a true equation. Proof Step 1: Substitute 3 for x in the original proportion. Proof Step 2: Cross multiply and simplify the result.
Example Solve this proportion for the value of x. Step 1: Cross multiply
Step 2: Divide both sides by 9 and simplify
Solution: Where , x = 2 Check the solution:
More Examples In each of the following examples:
Examples & Exercises


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