Chapter 19, Problem 1AR

Express each of the following fractions as equivalent fractions as indicated.
a. $\frac{3}{8}=\frac{?}{32}$
b. $\frac{7}{10}=\frac{?}{100}$
c. $\frac{1}{4}=\frac{?}{64}$
d. $\frac{9}{16}=\frac{?}{128}$

To determine

(a)

To express indicated fractions as equivalent fraction.

Answer to Problem 1AR

  $\frac{12}{32}$

Explanation of Solution

Given information:

A fractional equation is given as $\frac{3}{8}=\frac{?}{32}$.

Calculation:

We have been given a fractional equation as $\frac{3}{8}=\frac{?}{32}$.

Let us suppose

  $\begin{array}{l}\frac{3}{8}=\frac{x}{32}\\ \text{Applying cross multiplication,}\\ 3\times 32=x\times 8\\ \Rightarrow x=\frac{3\times 32}{8}\\ \Rightarrow x=\frac{3\times \cancel{8}\times 4}{\cancel{8}}\\ \Rightarrow x=12\end{array}$

Hence, equivalent fraction will be $\frac{x}{32}=\frac{12}{32}$.

To determine

(b)

To find equivalent fraction of indicated fraction.

Answer to Problem 1AR

  $\frac{70}{100}$

Explanation of Solution

Given information:

A fractional equation is given as $\frac{7}{10}=\frac{?}{100}$.

Calculation:

We have been given a fractional equation as $\frac{7}{10}=\frac{?}{100}$.

Let us suppose

  $\begin{array}{l}\frac{7}{10}=\frac{x}{100}\\ \text{Applying cross multiplication,}\\ 7\times 100=x\times 10\\ \Rightarrow x=\frac{7\times 100}{10}\\ \Rightarrow x=\frac{7\times \cancel{10}\times 10}{\cancel{10}}\\ \Rightarrow x=70\end{array}$

Hence, equivalent fraction will be $\frac{x}{100}=\frac{70}{100}$.

To determine

(c)

To evaluate equivalent fraction of indicated fraction.

Answer to Problem 1AR

  $\frac{16}{64}$

Explanation of Solution

Given information:

A fractional equation is given as $\frac{1}{4}=\frac{?}{64}$.

Calculation:

We have been given a fractional equation as $\frac{1}{4}=\frac{?}{64}$.

Let us suppose

  $\begin{array}{l}\frac{1}{4}=\frac{x}{64}\\ \text{Applying cross multiplication,}\\ 1\times 64=x\times 4\\ \Rightarrow x=\frac{1\times 64}{4}\\ \Rightarrow x=\frac{\cancel{4}\times 16}{\cancel{4}}\\ \Rightarrow x=16\end{array}$

Hence, equivalent fraction will be $\frac{x}{64}=\frac{16}{64}$.

To determine

(d)

To find equivalent fraction of indicated fraction.

Answer to Problem 1AR

  $\frac{72}{128}$

Explanation of Solution

Given information:

A fractional equation is given as $\frac{9}{16}=\frac{?}{128}$.

Calculation:

We have been given a fractional equation as $\frac{9}{16}=\frac{?}{128}$.

Let us suppose

  $\begin{array}{l}\frac{9}{16}=\frac{x}{128}\\ \text{Applying cross multiplication,}\\ 9\times 128=x\times 16\\ \Rightarrow x=\frac{9\times 128}{16}\\ \Rightarrow x=\frac{9\times \cancel{16}\times 8}{\cancel{16}}\\ \Rightarrow x=72\end{array}$

Hence, equivalent fraction will be $\frac{x}{128}=\frac{72}{128}$.