Similarity: Ratios and Proportions

Solving Proportions

 

We will be using proportions to solve real life problems.  Before we tackle that, let’s look at how we solve the proportion once it is set up.

To solve a proportion, we are looking for the value of the variable which makes the ratios equal.  Use the same process as we just used, cross multiply and then solve the equation.

Example:
Solve: seven-twelfths equals the fraction x over 72

Solution:
Start by cross multiplying.
seven-twelfths equals the fraction x over 72; 7 time 72 equals 12 x; 504 equals 12 x; 42 equals x

We can check this answer to see if the ratios are, indeed, equal.  We do this by substituting it into the original proportion.

seven-twelfths equals forty-two-seventy-seconds; 7 time 72 equals 12 times 42; 504 equals 504

The products are equal when you cross multiply, so the solution is correct.