Chapter 14, Problem 1A

Subtract $7\frac{5}{16}-2\frac{7}{8}$ .

To determine

To simplify the given expression.

Answer to Problem 1A

$4\frac{7}{16}$

Given information:

An expression is given as $7\frac{5}{16}-2\frac{7}{8}$.

Calculation:

We have been given an expression as $7\frac{5}{16}-2\frac{7}{8}$.

Converting mixed numbers into improper fraction.

$\begin{array}{l}7\frac{5}{16}-2\frac{7}{8}\\ =\left(7+\frac{5}{16}\right)-\left(2+\frac{7}{8}\right)\\ =\left(\frac{16\times 7+5}{16}\right)-\left(\frac{8\times 2+7}{8}\right)\\ =\frac{117}{16}-\frac{23}{8}\\ =\frac{117}{16}-\frac{23\times 2}{8\times 2}\text{ {Making denominator of both terms equal}}\\ =\frac{117}{16}-\frac{46}{16}\\ =\frac{117-46}{16}\\ =\frac{71}{16}\\ =4\frac{7}{16}\text{ {Converting improper fraction into mixed number}}\end{array}$

Explanation of Solution

Given information:

An expression is given as $7\frac{5}{16}-2\frac{7}{8}$.

Calculation:

We have been given an expression as $7\frac{5}{16}-2\frac{7}{8}$.

Converting mixed numbers into improper fraction.

$\begin{array}{l}7\frac{5}{16}-2\frac{7}{8}\\ =\left(7+\frac{5}{16}\right)-\left(2+\frac{7}{8}\right)\\ =\left(\frac{16\times 7+5}{16}\right)-\left(\frac{8\times 2+7}{8}\right)\\ =\frac{117}{16}-\frac{23}{8}\\ =\frac{117}{16}-\frac{23\times 2}{8\times 2}\text{ {Making denominator of both terms equal}}\\ =\frac{117}{16}-\frac{46}{16}\\ =\frac{117-46}{16}\\ =\frac{71}{16}\\ =4\frac{7}{16}\text{ {Converting improper fraction into mixed number}}\end{array}$