Chapter 6, Problem 8A

To determine

(a)

Solve the expression.

Answer to Problem 8A

The answer is $\frac{7}{2}$.

Explanation of Solution

Given:

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

Calculation:

The combined operations of the given expression are calculated as follows:

  $\begin{array}{c}=\frac{7}{9}\times \left(\frac{2}{3}+3\frac{5}{6}\right)\\ =\frac{7}{9}\times \left(\frac{2}{3}+\frac{23}{6}\right)\\ =\frac{7}{9}\times \left(\frac{4+23}{6}\right)\\ =\frac{7}{9}\times \frac{27}{6}\end{array}$

Simplify the above expression as follows:

  $\begin{array}{c}=7\times \frac{3}{6}\\ =7\times \frac{1}{2}\\ =\frac{7}{2}\end{array}$

Thus, the answer is $\frac{7}{2}$.

Conclusion:

The answer is $\frac{7}{2}$.

To determine

(b)

Solve the expression.

Answer to Problem 8A

The answer is $3\frac{11}{4}$.

Explanation of Solution

Given:

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

Calculation:

The combined operations of the given expression are calculated as follows:

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

Simplify the above expression as follows:

  $\begin{array}{c}=3+\frac{11}{4}\\ =\frac{12+11}{4}\\ =\frac{23}{4}\end{array}$

The mixed fraction of $\frac{23}{4}$ is $3\frac{11}{4}$.

Thus, the answer is $3\frac{11}{4}$.

Conclusion:

The answer is $3\frac{11}{4}$.

To determine

(c)

Solve the expression.

Answer to Problem 8A

The answer is $28\frac{3}{8}$.

Explanation of Solution

Given:

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

Calculation:

The combined operations of the given expression are calculated as follows:

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

Simplify the above expression as follows:

  $\begin{array}{c}=23+\frac{43}{8}\\ =\frac{184+43}{8}\\ =\frac{227}{8}\\ =28\frac{3}{8}\end{array}$

Thus, the answer is $28\frac{3}{8}$.

Conclusion:

The answer is $28\frac{3}{8}$.

To determine

(d)

Solve the expression.

Answer to Problem 8A

The answer is $3\frac{5}{6}$.

Explanation of Solution

Given:

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

Calculation:

The combined operations of the given expression are calculated as follows:

  $\begin{array}{c}=\left(16-4\frac{1}{2}\right)÷\left(\frac{1}{2}+2\frac{1}{8}\right)\\ =\left(16-\frac{9}{2}\right)÷\left(\frac{1}{2}+\frac{17}{8}\right)\\ =\left(\frac{32-9}{2}\right)÷\left(\frac{24}{8}\right)\\ =\frac{23}{2}÷3\end{array}$

Simplify the above expression as follows:

  $\begin{array}{c}=\frac{23}{2}\times \frac{1}{3}\\ =\frac{23}{6}\\ =3\frac{5}{6}\end{array}$

Thus, the answer is $3\frac{5}{6}$.

Conclusion:

The answer is $3\frac{5}{6}$.

To determine

(e)

Solve the expression.

Answer to Problem 8A

The answer is $20\frac{77}{87}$.

Explanation of Solution

Given:

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

Calculation:

The combined operations of the given expression are calculated as follows:

  $\begin{array}{c}=15\frac{1}{4}\times 1\frac{1}{3}+2\frac{2}{3}÷4\frac{5}{6}\\ =\frac{61}{4}\times \frac{4}{3}+\frac{8}{3}÷\frac{29}{6}\\ =\frac{61}{3}+\frac{8}{3}\times \frac{6}{29}\\ =\frac{61}{3}+\frac{16}{29}\end{array}$

Simplify the above expression as follows:

  $\begin{array}{c}=\frac{1769+48}{87}\\ =\frac{1817}{87}\\ =20\frac{77}{87}\end{array}$

Thus, the answer is $20\frac{77}{87}$.

Conclusion:

The answer is $20\frac{77}{87}$.