B1.04: Section 3

Example 1

Solve [latex]\frac{14}{3}=\frac{8}{x}[/latex].

Discussion: Sometimes students learn to solve problems like this one by “cross-multiplying.” That is correct. However, most math teachers prefer to think of solving this by multiplying both sides by the same thing—in this case the product of the two denominators. The result is the same. Both methods are shown below.

Example 2

Solve [latex]\frac{7}{33}=\frac{x}{5}[/latex]

Discussion: Here the variable isn’t in the denominator, but this illustrates that the basic principle of multiplying both sides by the same non-zero expression works here too.

Example 3

Solve [latex]\frac{12}{x}=6[/latex]

Example 4

Find a formula for h (that is, solve for h.) [latex]\frac{h}{36}=\frac{m}{k}[/latex].

Example 5

Find a formula for d (that is, solve for d.) [latex]\frac{a}{0.37}=\frac{r}{d}[/latex].