Chapter 6, Problem 7A

To determine

(a)

To solve the given expression.

Answer to Problem 7A

  $\frac{7}{16}$

Explanation of Solution

Given information:

An expression is given as $\frac{1}{2}+\frac{3}{16}-\frac{1}{4}$.

Calculation:

We have been given an expression as $\frac{1}{2}+\frac{3}{16}-\frac{1}{4}$.

Re-writing given expression by making a common denominator,

  $\begin{array}{l}\frac{1}{2}\times \frac{8}{8}+\frac{3}{16}-\frac{1}{4}\times \frac{4}{4}\\ =\frac{8}{16}+\frac{3}{16}-\frac{4}{16}\\ =\frac{8+3-4}{16}\\ =\frac{7}{16}\end{array}$

Hence, $\frac{1}{2}+\frac{3}{16}-\frac{1}{4}$$=$ $\frac{7}{16}$

To determine

(b)

To solve the given expression.

Answer to Problem 7A

  $2\frac{1}{16}$

Explanation of Solution

Given information:

An expression is given as $3\frac{7}{8}-2\frac{3}{16}+\frac{3}{8}$.

Calculation:

We have been given an expression as $3\frac{7}{8}-2\frac{3}{16}+\frac{3}{8}$.

First convert mixed number into improper function,

  $3\frac{7}{8}-2\frac{3}{16}+\frac{3}{8}=\frac{31}{8}-\frac{35}{16}+\frac{3}{8}$

Re-writing given expression by making a common denominator,

  $\begin{array}{l}=\frac{31}{8}\times \frac{2}{2}-\frac{35}{16}+\frac{3}{8}\times \frac{2}{2}\\ =\frac{62}{16}-\frac{35}{16}+\frac{6}{16}\\ =\frac{62-35+6}{16}\\ =\frac{33}{16}=2\frac{1}{16}\end{array}$

Hence, $3\frac{7}{8}-2\frac{3}{16}+\frac{3}{8}$$=$ $2\frac{1}{16}$

To determine

(c)

To solve the given expression.

Answer to Problem 7A

  $5\frac{33}{50}$

Explanation of Solution

Given information:

An expression is given as $\frac{3}{10}+8\frac{2}{5}-3\frac{1}{25}$.

Calculation:

We have been given an expression as $\frac{3}{10}+8\frac{2}{5}-3\frac{1}{25}$.

First convert mixed number into improper function,

  $\frac{3}{10}+8\frac{2}{5}-3\frac{1}{25}=\frac{3}{10}+\frac{42}{5}-\frac{76}{25}$

Re-writing given expression by making a common denominator,

  $\begin{array}{l}=\frac{3}{10}\times \frac{5}{5}+\frac{42}{5}\times \frac{10}{10}-\frac{76}{25}\times \frac{2}{2}\\ =\frac{15}{50}+\frac{420}{50}-\frac{152}{50}\\ =\frac{15+420-152}{50}\\ =\frac{283}{50}=5\frac{33}{50}\end{array}$

Hence, $\frac{3}{10}+8\frac{2}{5}-3\frac{1}{25}$$=$ $5\frac{33}{50}$

To determine

(d)

To solve the given expression.

Answer to Problem 7A

  $28\frac{1}{2}$

Explanation of Solution

Given information:

An expression is given as $27-2\frac{2}{3}+4\frac{1}{6}$.

Calculation:

We have been given an expression as $27-2\frac{2}{3}+4\frac{1}{6}$.

First convert mixed number into improper function,

  $27-2\frac{2}{3}+4\frac{1}{6}=27-\frac{8}{3}+\frac{25}{6}$

Re-writing given expression by making a common denominator,

  $\begin{array}{l}=27\times \frac{6}{6}-\frac{8}{3}\times \frac{2}{2}+\frac{25}{6}\\ =\frac{162}{6}-\frac{16}{6}+\frac{25}{6}\\ =\frac{162-16+25}{6}\\ =\frac{171}{6}=28\frac{3}{6}=28\frac{1}{2}\end{array}$

Hence, $27-2\frac{2}{3}+4\frac{1}{6}$$=$ $28\frac{1}{2}$

To determine

(e)

To solve the given expression.

Answer to Problem 7A

  $33\frac{49}{64}$

Explanation of Solution

Given information:

An expression is given as $32\frac{1}{8}+2\frac{3}{16}\times \frac{3}{4}$.

Calculation:

We have been given an expression as $32\frac{1}{8}+2\frac{3}{16}\times \frac{3}{4}$.

First convert mixed number into improper function,

  $32\frac{1}{8}+2\frac{3}{16}\times \frac{3}{4}=\frac{257}{8}+\frac{35}{16}\times \frac{3}{4}=\frac{257}{8}+\frac{105}{64}$

Re-writing given expression by making a common denominator,

  $\begin{array}{l}=\frac{257}{8}\times \frac{8}{8}+\frac{105}{64}\\ =\frac{2056}{64}+\frac{105}{64}\\ =\frac{2056+105}{64}\\ =\frac{2161}{64}=33\frac{49}{64}\end{array}$

Hence, $32\frac{1}{8}+2\frac{3}{16}\times \frac{3}{4}$$=$ $33\frac{49}{64}$

To determine

(f)

To solve the given expression.

Answer to Problem 7A

  $3\frac{1}{2}$

Explanation of Solution

Given information:

An expression is given as $\frac{7}{9}\times \left(\frac{2}{3}+3\frac{5}{6}\right)$.

Calculation:

We have been given an expression as $\frac{7}{9}\times \left(\frac{2}{3}+3\frac{5}{6}\right)$.

First convert mixed number into improper function,

  $\frac{7}{9}\times \left(\frac{2}{3}+3\frac{5}{6}\right)=\frac{7}{9}\times \left(\frac{2}{3}+\frac{23}{6}\right)$

Re-writing given expression by making a common denominator,

  $\begin{array}{l}=\frac{7}{9}\times \left(\frac{2}{3}\times \frac{2}{2}+\frac{23}{6}\right)\\ =\frac{7}{9}\times \left(\frac{4}{6}+\frac{23}{6}\right)\\ =\frac{7}{9}\times \left(\frac{4+23}{6}\right)\\ =\frac{7}{9}\times \frac{27}{6}=\frac{7}{2}=3\frac{1}{2}\end{array}$

Hence, $\frac{7}{9}\times \left(\frac{2}{3}+3\frac{5}{6}\right)$$=$ $3\frac{1}{2}$

To determine

(g)

To solve the given expression.

Answer to Problem 7A

  $3\frac{1}{2}$

Explanation of Solution

Given information:

An expression is given as $12-4\frac{1}{2}÷\frac{1}{2}+2\frac{3}{4}$.

Calculation:

We have been given an expression as $12-4\frac{1}{2}÷\frac{1}{2}+2\frac{3}{4}$.

First convert mixed number into improper function,

  $\begin{array}{l}12-4\frac{1}{2}÷\frac{1}{2}+2\frac{3}{4}\\ =12-\frac{9}{2}÷\frac{1}{2}+\frac{11}{4}\\ =12-\frac{9}{2}\times \frac{2}{1}+\frac{11}{4}\\ =12-9+\frac{11}{4}\\ =3+\frac{11}{4}\\ =\frac{12+11}{4}\\ =\frac{23}{4}\\ =5\frac{3}{4}\end{array}$

Hence, $12-4\frac{1}{2}÷\frac{1}{2}+2\frac{3}{4}$$=$ $5\frac{3}{4}$

To determine

(h)

To solve the given expression.

Answer to Problem 7A

  $28\frac{3}{8}$

Explanation of Solution

Given information:

An expression is given as $\left(16-4\frac{1}{2}\right)÷\frac{1}{2}+5\frac{3}{8}$.

Calculation:

We have been given an expression as $\left(16-4\frac{1}{2}\right)÷\frac{1}{2}+5\frac{3}{8}$.

First convert mixed number into improper function,

  $\begin{array}{l}\left(16-4\frac{1}{2}\right)÷\frac{1}{2}+5\frac{3}{8}\\ =\left(16-\frac{9}{2}\right)÷\frac{1}{2}+\frac{43}{8}\\ =\left(\frac{32-9}{2}\right)÷\frac{1}{2}+\frac{43}{8}\\ =\frac{23}{2}\times \frac{2}{1}+\frac{43}{8}\\ =23+\frac{43}{8}\\ =\frac{23\times 8+43}{8}\\ =\frac{227}{8}\\ =28\frac{3}{8}\end{array}$

Hence, $\left(16-4\frac{1}{2}\right)÷\frac{1}{2}+5\frac{3}{8}$$=$ $28\frac{3}{8}$

To determine

(i)

To solve the given expression.

Answer to Problem 7A

  $28\frac{3}{8}$

Explanation of Solution

Given information:

An expression is given as $\left(16-4\frac{1}{2}\right)÷\left(\frac{1}{2}+2\frac{1}{8}\right)$.

Calculation:

We have been given an expression as $\left(16-4\frac{1}{2}\right)÷\left(\frac{1}{2}+2\frac{1}{8}\right)$.

First convert mixed number into improper function,

  $\begin{array}{l}\left(16-4\frac{1}{2}\right)÷\left(\frac{1}{2}+2\frac{1}{8}\right)\\ =\left(16-\frac{9}{2}\right)÷\left(\frac{1}{2}+\frac{17}{8}\right)\\ =\left(\frac{32-9}{2}\right)÷\left(\frac{4+17}{8}\right)\\ =\frac{23}{2}÷\frac{21}{8}\\ =\frac{23}{2}\times \frac{8}{21}\\ =\frac{92}{21}\\ =4\frac{8}{21}\end{array}$

Hence, $\left(16-4\frac{1}{2}\right)÷\left(\frac{1}{2}+2\frac{1}{8}\right)$$=$ $4\frac{8}{21}$

To determine

(j)

To solve the given expression.

Answer to Problem 7A

  $20\frac{77}{87}$

Explanation of Solution

Given information:

An expression is given as $15\frac{1}{4}\times 1\frac{1}{3}+2\frac{2}{3}÷4\frac{5}{6}$.

Calculation:

We have been given an expression as $15\frac{1}{4}\times 1\frac{1}{3}+2\frac{2}{3}÷4\frac{5}{6}$.

First convert mixed number into improper function,

  $\begin{array}{l}15\frac{1}{4}\times 1\frac{1}{3}+2\frac{2}{3}÷4\frac{5}{6}\\ =\frac{61}{4}\times \frac{4}{3}+\frac{8}{3}÷\frac{29}{6}\\ =\frac{61}{4}\times \frac{4}{3}+\frac{8}{3}\times \frac{6}{29}\\ =\frac{61}{3}\times \frac{16}{29}\\ =\frac{61\times 29+16\times 3}{87}\\ =\frac{1769+48}{87}\\ =\frac{1817}{87}\\ =20\frac{77}{87}\end{array}$

Hence, $15\frac{1}{4}\times 1\frac{1}{3}+2\frac{2}{3}÷4\frac{5}{6}$$=$ $20\frac{77}{87}$