Chapter 6.7, Problem 2E

To determine

To simplify: the expression $\frac{\frac{3a}{4}}{\frac{15a}{12}}$.

Answer to Problem 2E

  $\frac{3}{5}$.

Explanation of Solution

Given information:

  $\frac{\frac{3a}{4}}{\frac{15a}{12}}$

Formula used:

Method 1.

Simplify the numerator and denominator . Then express the fraction as quotient using the ÷ sign. Multiply by the reciprocal of the divisor.

Method 2.

Find the LCD of all simple fractions . Multiply the numerator and the denominator of the complex fraction by the LCD.

Calculation:

Consider ,

  $\frac{\frac{3a}{4}}{\frac{15a}{12}}$

Now,

  $=\frac{\frac{3a}{4}}{\frac{15a}{12}}=\frac{3a}{4}÷\frac{15a}{12}$

  $\begin{array}{l}=\frac{3a}{4}\times \frac{12}{15a}\\ =\frac{3}{5}\end{array}$

Thus, the solution is $\frac{3}{5}$.