Chapter 11.3, Problem 68MR

To determine

To simplify:

  $\frac{4}{9}+\frac{2}{9}$

Answer to Problem 68MR

  $\frac{4}{9}+\frac{2}{9}=\frac{2}{3}$

Explanation of Solution

Given:

  $\frac{4}{9}+\frac{2}{9}$

Concept Used:

• Addition/subtraction of two fractions with equal numerator is done as:

  $\frac{a}{b}\pm \frac{c}{b}=\frac{a\pm c}{b},b\ne 0$

Calculation:

In order to simplify:

  $\frac{4}{9}+\frac{2}{9}$

Use the formula:

  $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b},b\ne 0$

As,

  $\begin{array}{c}\frac{4}{9}+\frac{2}{9}=\frac{4+2}{9}\\ =\frac{6}{9}\end{array}$

Again simplify the fraction by canceling the common factor of numerator and denominator, as

  $\begin{array}{c}\frac{6}{9}=\frac{3\cdot 2}{3\cdot 3}\\ =\frac{2}{3}\end{array}$

Thus,

  $\frac{4}{9}+\frac{2}{9}=\frac{2}{3}$