Chapter 1.3, Problem 19PPS

To determine

To evaluate the expression:

  $3\frac{2}{3}+4+5\frac{1}{3}$

Answer to Problem 19PPS

  $3\frac{2}{3}+4+5\frac{1}{3}=13$

Explanation of Solution

Given:

  $3\frac{2}{3}+4+5\frac{1}{3}$

Concept Used:

• A mixed fraction $a\frac{b}{c}$ can be written in a simple fraction as $a\frac{b}{c}=\frac{ac+b}{c}$ where a,b and c are integers.
• Commutative property of addition: $a+b=b+a$
• Addition of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are done as

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

Calculation:

In order to evaluate the expression

  $3\frac{2}{3}+4+5\frac{1}{3}$

First, simplify the mixed fractions in the expression

As,

  $\begin{array}{c}3\frac{2}{3}+4+5\frac{1}{3}=\left[\frac{\left(3\times 3\right)+2}{3}\right]+4+\left[\frac{\left(3\times 5\right)+1}{3}\right]\\ =\left[\frac{9+2}{3}\right]+4+\left[\frac{15+1}{3}\right]\\ =\frac{11}{3}+4+\frac{16}{3}\\ =\frac{11}{3}+\frac{16}{3}+4,\text{ commutative property}\text{.}\\ \text{=}\frac{11+16}{3}+4\\ \text{=}\frac{27}{3}+4,\text{ division}\\ =9+4,addition\\ =13\end{array}$

Thus,

  $3\frac{2}{3}+4+5\frac{1}{3}=13$