Chapter 19, Problem 7AR

To determine

(a)

To evaluate the given expression.

Answer to Problem 7AR

  $\frac{5}{16}$

Explanation of Solution

Given information:

An expression is given as $\frac{1}{2}\times \frac{5}{8}$

Calculation:

We have been given an expression as $\frac{1}{2}\times \frac{5}{8}$.

Evaluating the expression,

  $\begin{array}{l}\frac{1}{2}\times \frac{5}{8}=\frac{1\times 5}{2\times 8}\\ =\frac{5}{16}\end{array}$

Hence, $\frac{1}{2}\times \frac{5}{8}$$=$$\frac{5}{16}$.

To determine

(b)

To multiply the given fractions.

Answer to Problem 7AR

  $\frac{2}{5}$

Explanation of Solution

Given information:

An expression is given as $\frac{3}{4}\times \frac{4}{5}\times \frac{2}{3}$

Calculation:

We have been given an expression as $\frac{3}{4}\times \frac{4}{5}\times \frac{2}{3}$.

Evaluating the expression,

  $\begin{array}{l}\frac{3}{4}\times \frac{4}{5}\times \frac{2}{3}\\ =\frac{\cancel{3}}{\cancel{4}}\times \frac{\cancel{4}}{5}\times \frac{2}{\cancel{3}}\\ =\frac{2}{5}\end{array}$

Hence, $\frac{3}{4}\times \frac{4}{5}\times \frac{2}{3}$$=$$\frac{2}{5}$.

To determine

(c)

To evaluate the given expression.

Answer to Problem 7AR

  $1\frac{245}{256}$

Explanation of Solution

Given information:

An expression is given as $5\frac{7}{32}\times \frac{3}{8}$

Calculation:

We have been given an expression as $5\frac{7}{32}\times \frac{3}{8}$.

Evaluating the expression,

  $\begin{array}{l}5\frac{7}{32}\times \frac{3}{8}=\frac{5\times 32+7}{32}\times \frac{3}{8}\\ =\frac{167}{32}\times \frac{3}{8}\\ =\frac{501}{256}=1\frac{245}{256}\end{array}$

Hence, $5\frac{7}{32}\times \frac{3}{8}$$=$$1\frac{245}{256}$.

To determine

(d)

To find the simplified value of given fractions.

Answer to Problem 7AR

  $\frac{1023}{40}$

Explanation of Solution

Given information:

An expression is given as $3\frac{1}{10}\times 8\frac{1}{4}$

Calculation:

We have been given an expression as $3\frac{1}{10}\times 8\frac{1}{4}$.

Evaluating the expression,

  $\begin{array}{l}3\frac{1}{10}\times 8\frac{1}{4}=\frac{3\times 10+1}{10}\times \frac{8\times 4+1}{4}\\ =\frac{31}{10}\times \frac{33}{4}\\ =\frac{1023}{40}\end{array}$

Hence, $3\frac{1}{10}\times 8\frac{1}{4}$$=$$\frac{1023}{40}$.

To determine

(e)

To evaluate the given expression.

Answer to Problem 7AR

  $\frac{165}{8}$

Explanation of Solution

Given information:

An expression is given as $\frac{3}{16}\times 20\times 5\frac{1}{2}$

Calculation:

We have been given an expression as $\frac{3}{16}\times 20\times 5\frac{1}{2}$.

Evaluating the expression,

  $\begin{array}{l}\frac{3}{16}\times 20\times 5\frac{1}{2}=\frac{3}{16}\times 20\times \frac{5\times 2+1}{2}\\ =\frac{3}{16}\times 20\times \frac{11}{2}=\frac{3}{\cancel{4}\times 4}\times \cancel{4}\times 5\times \frac{11}{2}\\ =\frac{165}{8}\end{array}$

Hence, $\frac{3}{16}\times 20\times 5\frac{1}{2}$$=$$\frac{165}{8}$.

To determine

(f)

To divide the given fractions.

Answer to Problem 7AR

  $\frac{3}{4}$

Explanation of Solution

Given information:

An expression is given as $\frac{3}{10}÷\frac{2}{5}$

Calculation:

We have been given an expression as $\frac{3}{10}÷\frac{2}{5}$.

Evaluating the expression,

  $\begin{array}{l}\frac{3}{10}÷\frac{2}{5}=\frac{3}{10}\times \frac{5}{2}\\ =\frac{3\times \cancel{5}}{\cancel{5}\times 2\times 2}\\ =\frac{3}{4}\end{array}$

Hence, $\frac{3}{10}÷\frac{2}{5}$$=$$\frac{3}{4}$.

To determine

(g)

To divide the given fractions.

Answer to Problem 7AR

  $\frac{3}{4}$

Explanation of Solution

Given information:

An expression is given as $\frac{14}{15}÷\frac{7}{25}$

Calculation:

We have been given an expression as $\frac{14}{15}÷\frac{7}{25}$.

Evaluating the expression,

  $\begin{array}{l}\frac{14}{15}÷\frac{7}{25}=\frac{14}{15}\times \frac{25}{7}\\ =\frac{\cancel{7}\times 2}{3\times \cancel{5}}\times \frac{5\times \cancel{5}}{\cancel{7}}\\ =\frac{10}{3}\end{array}$

Hence, $\frac{14}{15}÷\frac{7}{25}$$=$$\frac{10}{3}$.

To determine

(h)

To find the simplified value of given expression.

Answer to Problem 7AR

  $48$

Explanation of Solution

Given information:

An expression is given as $16÷\frac{1}{3}$

Calculation:

We have been given an expression as $16÷\frac{1}{3}$.

Evaluating the expression,

  $\begin{array}{l}16÷\frac{1}{3}=16\times \frac{3}{1}\\ =48\end{array}$

Hence, $16÷\frac{1}{3}$$=$$48$.

To determine

(i)

To find the simplified value of given expression.

Answer to Problem 7AR

  $\frac{27}{4}$

Explanation of Solution

Given information:

An expression is given as $2\frac{17}{32}÷\frac{9}{24}$

Calculation:

We have been given an expression as $2\frac{17}{32}÷\frac{9}{24}$.

Evaluating the expression,

  $\begin{array}{l}2\frac{17}{32}÷\frac{9}{24}=\frac{2\times 32+17}{32}÷\frac{9}{24}\\ =\frac{81}{32}\times \frac{24}{9}=\frac{9\times \cancel{9}}{\cancel{8}\times 4}\times \frac{\cancel{8}\times 3}{\cancel{9}}\\ =\frac{27}{4}\end{array}$

Hence, $2\frac{17}{32}÷\frac{9}{24}$$=$$\frac{27}{4}$.

To determine

(j)

To find the simplified value of given expression.

Answer to Problem 7AR

  $\frac{125}{32}$

Explanation of Solution

Given information:

An expression is given as $2\frac{29}{32}÷8\frac{3}{4}$

Calculation:

We have been given an expression as $2\frac{29}{32}÷8\frac{3}{4}$.

Evaluating the expression,

  $\begin{array}{l}2\frac{29}{32}÷8\frac{3}{4}=\frac{2\times 32+29}{32}÷\frac{8\times 4+3}{4}\\ =\frac{93}{32}÷\frac{33}{4}=\frac{\cancel{3}\times 31}{8\times \cancel{4}}\times \frac{\cancel{4}}{\cancel{3}\times 11}\\ =\frac{31}{88}\end{array}$

Hence, $2\frac{29}{32}÷8\frac{3}{4}$$=$$\frac{31}{88}$.