Chapter 1, Problem 16A

Express the improper fractions in Exercises 15 and 16 as mixed numbers.
16.
a. $\frac{127}{32}$
b. $\frac{57}{15}$
c. $\frac{150}{9}$
d. $\frac{235}{16}$
e. $\frac{514}{4}$
f. $\frac{401}{64}$

To determine

(a)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{127}{32}$ is $3\frac{31}{32}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{127}{32}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $127$ with denominator $32$ as follows:

  $32\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}127\\ -\underset{\_}{096}\\ 031\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{31}{32}$.

Add $3$ with $\frac{31}{32}$ as follows:

  $\begin{array}{l}=3+\frac{31}{32}\\ =3\frac{31}{32}\end{array}$

Thus, the mixed number of $\frac{127}{32}$ is $3\frac{31}{32}$.

Conclusion:

The mixed number of $\frac{127}{32}$ is $3\frac{31}{32}$.

To determine

(b)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{57}{15}$ is $3\frac{12}{15}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{57}{15}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $57$ with denominator $15$ as follows:

  $15\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}57\\ -\underset{\_}{45}\\ 12\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{12}{15}$.

Add $3$ with $\frac{12}{15}$ as follows:

  $\begin{array}{l}=3+\frac{12}{15}\\ =3\frac{12}{15}\end{array}$

Thus, the mixed number of $\frac{57}{15}$ is $3\frac{12}{15}$.

Conclusion:

The mixed number of $\frac{57}{15}$ is $3\frac{12}{15}$.

To determine

(c)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{150}{9}$ is $16\frac{6}{9}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{150}{9}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $150$ with denominator $9$ as follows:

  $9\begin{array}{c}\hfill 16\\ \hfill \overline{)\begin{array}{l}150\\ -\underset{\_}{09}\\ 060\\ -\underset{\_}{054}\\ 6\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{6}{9}$.

Add $16$ with $\frac{6}{9}$ as follows:

  $\begin{array}{l}=16+\frac{6}{9}\\ =16\frac{6}{9}\end{array}$

Thus, the mixed number of $\frac{150}{9}$ is $16\frac{6}{9}$.

Conclusion:

The mixed number of $\frac{150}{9}$ is $16\frac{6}{9}$.

To determine

(d)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{235}{16}$ is $14\frac{11}{16}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{235}{16}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $235$ with denominator $16$ as follows:

  $16\begin{array}{c}\hfill 14\\ \hfill \overline{)\begin{array}{l}235\\ -\underset{\_}{16}\\ 075\\ -\underset{\_}{064}\\ 11\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{11}{16}$.

Add $14$ with $\frac{11}{16}$ as follows:

  $\begin{array}{l}=14+\frac{11}{16}\\ =14\frac{11}{16}\end{array}$

Thus, the mixed number of $\frac{235}{16}$ is $14\frac{11}{16}$.

Conclusion:

The mixed number of $\frac{235}{16}$ is $14\frac{11}{16}$.

To determine

(e)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{514}{4}$ is $128\frac{2}{4}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{514}{4}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $514$ with denominator $4$ as follows:

  $4\begin{array}{c}\hfill 128\\ \hfill \overline{)\begin{array}{l}514\\ -\underset{\_}{4}\\ 11\\ -\underset{\_}{08}\\ 34\\ -\underset{\_}{32}\\ 2\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{2}{4}$.

Add $128$ with $\frac{2}{4}$ as follows:

  $\begin{array}{l}=128+\frac{2}{4}\\ =128\frac{2}{4}\end{array}$

Thus, the mixed number of $\frac{514}{4}$ is $128\frac{2}{4}$.

Conclusion:

The mixed number of $\frac{514}{4}$ is $128\frac{2}{4}$.

To determine

(f)

Express the fraction as a mixed number.

Answer to Problem 16A

The mixed number of $\frac{401}{64}$ is $6\frac{17}{64}$.

Explanation of Solution

Given:

The given mixed fraction is $\frac{401}{64}$.

Concept used:

Divide the numerator and denominator. The ratio of the remainder and divisor is expressed as a fraction. The obtained fraction is then added to quotient.

Calculation:

Divide the numerator $401$ with denominator $64$ as follows:

  $64\begin{array}{c}\hfill 6\\ \hfill \overline{)\begin{array}{l}401\\ -\underset{\_}{384}\\ 017\end{array}}\end{array}$

Therefore, the number to be added to quotient is $\frac{17}{64}$.

Add $6$ with $\frac{17}{64}$ as follows:

  $\begin{array}{l}=6+\frac{17}{64}\\ =6\frac{17}{64}\end{array}$

Thus, the mixed number of $\frac{401}{64}$ is $6\frac{17}{64}$.

Conclusion:

The mixed number of $\frac{401}{64}$ is $6\frac{17}{64}$.