Chapter 1.3, Problem 20PPS

To determine

To evaluate the expression:

  $4\frac{4}{9}+7\frac{2}{9}$ , and to name the property used.

Answer to Problem 20PPS

  $4\frac{4}{9}+7\frac{2}{9}=\frac{105}{9}$

And the property used is addition property of fractions having same denominator.

Explanation of Solution

Given:

  $4\frac{4}{9}+7\frac{2}{9}$

Concept Used:

Addition property of fractions having same denominator:

  $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

Calculation:

In order to evaluate the expression

  $4\frac{4}{9}+7\frac{2}{9}$

First simplify mixed fraction and then add using the property of sum of fractions having same denominators

  $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$

As,

  $\begin{array}{c}4\frac{4}{9}+7\frac{2}{9}=\frac{40}{9}+\frac{65}{9}\\ =\frac{40+65}{9}\\ =\frac{105}{9}\end{array}$

Thus,

  $4\frac{4}{9}+7\frac{2}{9}=\frac{105}{9}$

And the property used is addition property of fractions having same denominator.