Chapter 0.4, Problem 23E

To determine

To find: The simplest form of the given sum or difference.

Answer to Problem 23E

The simplest form of the difference is $\frac{17}{30}$ .

Explanation of Solution

Given:

The given difference is $\frac{7}{10}-\frac{2}{15}$ .

Calculation:

Consider the given difference,

  $\frac{7}{10}-\frac{2}{15}$

Consider the factors of 10 is,

  $10=5\times 2$

Consider the factors of 15 is,

  $15=3\times 5$

Consider the LCM of 10 and 15 is,

  $2\times 5\times 3=30$

Consider the fraction $\frac{7}{10}$ as,

  $\begin{array}{c}\frac{7}{10}=\frac{7\times 3}{10\times 3}\\ =\frac{21}{30}\end{array}$

Consider the fraction $\frac{2}{15}$ as,

  $\begin{array}{c}\frac{2}{15}=\frac{2\times 2}{15\times 2}\\ =\frac{4}{30}\end{array}$

Then, the difference is,

  $\begin{array}{c}\frac{21}{30}-\frac{4}{30}=\frac{21-4}{30}\\ =\frac{17}{30}\end{array}$