Chapter 4, Problem 13A

To determine

(a)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $10\frac{1}{2}$.

Explanation of Solution

Given:

The number is $1\frac{2}{3}\times 6\frac{3}{10}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number $1\frac{2}{3}$ is $\frac{5}{3}$.

The improper fraction of $6\frac{3}{10}$ is $\frac{63}{10}$.

Multiply $\frac{5}{3}\times \frac{63}{10}$ as follows:

Multiply the numerators $5$ and $63$.

  $\begin{array}{c}=5\times 63\\ =315\end{array}$

Multiply the denominators $3$ and $10$.

  $\begin{array}{c}=3\times 10\\ =30\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{315}{30}$

The greatest common factor of $315$ and $30$ is $15$.

Divide numerator and denominator of fraction by $15$.

  $\begin{array}{c}=\frac{315÷15}{30÷15}\\ =\frac{21}{2}\end{array}$

The mixed conversion of $\frac{21}{2}$ is as follows:

  $2\begin{array}{c}\hfill 10\\ \hfill \overline{)\begin{array}{l}21\\ -\underset{\_}{2}\\ 01\end{array}}\end{array}$

The mixed conversion of $\frac{21}{2}$ is $10\frac{1}{2}$.

Thus, the multiplication of fractions is $10\frac{1}{2}$.

Conclusion:

The multiplication of fractions is $10\frac{1}{2}$.

To determine

(b)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $25\frac{43}{64}$.

Explanation of Solution

Given:

The number is $3\frac{5}{16}\times 7\frac{3}{4}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number $3\frac{5}{16}$ is $\frac{53}{16}$.

The improper fraction of $7\frac{3}{4}$ is $\frac{31}{4}$.

Multiply $\frac{53}{16}\times \frac{31}{4}$ as follows:

Multiply the numerators $53$ and $31$.

  $\begin{array}{c}=53\times 31\\ =1643\end{array}$

Multiply the denominators $16$ and $4$.

  $\begin{array}{c}=16\times 4\\ =64\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{1643}{64}$

The mixed conversion of $\frac{1643}{64}$ is as follows:

  $\begin{array}{l}64\begin{array}{c}\hfill 25\\ \hfill \overline{)\begin{array}{l}1643\\ -\underset{\_}{128}\end{array}}\end{array}\end{array}$

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The mixed conversion of $\frac{1643}{64}$ is $25\frac{43}{64}$.

Thus, the multiplication of fractions is $25\frac{43}{64}$.

Conclusion:

The multiplication of fractions is $25\frac{43}{64}$.

To determine

(c)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $11\frac{9}{16}$.

Explanation of Solution

Given:

The number is $4\frac{5}{8}\times 2\frac{1}{2}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number $4\frac{5}{8}$ is $\frac{37}{8}$.

The improper fraction of $2\frac{1}{2}$ is $\frac{5}{2}$.

Multiply $\frac{37}{8}\times \frac{5}{2}$ as follows:

Multiply the numerators $37$ and $5$.

  $\begin{array}{c}=37\times 5\\ =185\end{array}$

Multiply the denominators $8$ and $2$.

  $\begin{array}{c}=8\times 2\\ =16\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{185}{16}$

The mixed conversion of $\frac{185}{16}$ is as follows:

  $16\begin{array}{c}\hfill 11\\ \hfill \overline{)\begin{array}{l}185\\ -\underset{\_}{16}\\ 025\\ -\underset{\_}{16}\\ 9\end{array}}\end{array}$

The mixed conversion of $\frac{185}{16}$ is $11\frac{9}{16}$.

Thus, the multiplication of fractions is $11\frac{9}{16}$.

Conclusion:

The multiplication of fractions is $11\frac{9}{16}$.

To determine

(d)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $6\frac{13}{32}$.

Explanation of Solution

Given:

The number is $1\frac{2}{3}\times 10\frac{1}{4}\times \frac{3}{8}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number $1\frac{2}{3}$ is $\frac{5}{3}$.

The improper fraction of $10\frac{1}{4}$ is $\frac{41}{4}$.

The third is already in improper fraction that is $\frac{3}{8}$.

Multiply $\frac{5}{3}\times \frac{41}{4}\times \frac{3}{8}$ as follows:

Multiply the numerators $5$, $41$ and $3$.

  $\begin{array}{c}=5\times 41\times 3\\ =615\end{array}$

Multiply the denominators $3$, $4$ and $8$.

  $\begin{array}{c}=3\times 4\times 8\\ =96\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{615}{96}$

The greatest common factor of $615$ and $96$ is $3$.

Divide numerator and denominator of fraction by $3$.

  $\begin{array}{c}=\frac{615÷3}{96÷3}\\ =\frac{205}{32}\end{array}$

The mixed conversion of $\frac{205}{32}$ is as follows:

  $32\begin{array}{c}\hfill 6\\ \hfill \overline{)\begin{array}{l}205\\ -\underset{\_}{192}\\ 013\end{array}}\end{array}$

The mixed conversion of $\frac{205}{32}$ is $6\frac{13}{32}$.

Thus, the multiplication of fractions is $6\frac{13}{32}$.

Conclusion:

The multiplication of fractions is $6\frac{13}{32}$.

To determine

(e)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $\frac{201}{256}$.

Explanation of Solution

Given:

The number is $2\frac{3}{32}\times 3\times \frac{1}{8}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of mixed number $2\frac{3}{32}$ is $\frac{67}{32}$.

The second number is $3$.

The third is already in improper fraction that is $\frac{1}{8}$.

Multiply $\frac{67}{32}\times 3\times \frac{1}{8}$ as follows:

Multiply the numerators $67$, $3$ and $1$.

  $\begin{array}{c}=67\times 3\times 1\\ =201\end{array}$

Multiply the denominators $32$ and $8$.

  $\begin{array}{c}=32\times 8\\ =256\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{201}{256}$

Thus, the multiplication of fractions is $\frac{201}{256}$.

Conclusion:

The multiplication of fractions is $\frac{201}{256}$.

To determine

(f)

Multiply the mixed fractions and reduce to lowest term.

Answer to Problem 13A

The multiplication of fractions is $37\frac{1}{3}$.

Explanation of Solution

Given:

The number is $2\frac{2}{3}\times 2\frac{2}{3}\times 5\frac{1}{4}$.

Concept used:

Convert mixed fraction into improper fractions. Multiply all the numerators and denominators of all fractions with each other to get the product and reduce it to lowest form by greatest common factor.

Calculation:

The improper fraction of first mixed number $2\frac{2}{3}$ is $\frac{8}{3}$.

The improper fraction of second mixed number $2\frac{2}{3}$ is $\frac{8}{3}$.

The improper fraction of third mixed number $5\frac{1}{4}$ is $\frac{21}{4}$.

Multiply $\frac{8}{3}\times \frac{8}{3}\times \frac{21}{4}$ as follows:

Multiply the numerators $8$, $8$ and $21$.

  $\begin{array}{c}=8\times 8\times 21\\ =1344\end{array}$

Multiply the denominators $3$, $3$ and $4$.

  $\begin{array}{c}=3\times 3\times 4\\ =36\end{array}$

Therefore, the multiplication of fractions is as follows:

  $=\frac{1344}{36}$

The greatest common factor of $1344$ and $36$ is $12$.

Divide numerator and denominator of fraction by $12$.

  $\begin{array}{c}=\frac{1344÷12}{36÷12}\\ =\frac{112}{3}\end{array}$

The mixed conversion of $\frac{112}{3}$ is as follows:

  $3\begin{array}{c}\hfill 37\\ \hfill \overline{)\begin{array}{l}112\\ -\underset{\_}{09}\\ 022\\ -\underset{\_}{21}\\ 01\end{array}}\end{array}$

The mixed conversion of $\frac{112}{3}$ is $37\frac{1}{3}$.

Thus, the multiplication of fractions is $37\frac{1}{3}$.

Conclusion:

The multiplication of fractions is $37\frac{1}{3}$.