Chapter 7.2, Problem 23E

To determine

To calculate: The equivalent percent for each fraction.

Answer to Problem 23E

  

Explanation of Solution

Given information:

The table given in the question:

  

Concept used:

  $\begin{array}{l}\text{Represent }"a\text{ is }p\text{ percent of }b\text{" using the proportion}\\ \frac{a}{b}=\frac{p}{100}\\ \text{where }a\text{ is a part of the base }b\text{ and }p\text{\%,or }\frac{p}{100},\text{ is the percent}\text{.}\end{array}$

Calculation:

As per the problem

1.Consider the fraction $\frac{1}{8}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $1\text{ for }a\text{ and 8 for }b$ ,

  $\frac{1}{8}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 1=p\cdot 8$

Simplify,

  $100=8p$ .

Divide each side by $8$ and simplify

  $12.5=p$

2. Consider the fraction $\frac{1}{3}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $1\text{ for }a\text{ and 3 for }b$ ,

  $\frac{1}{3}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 1=p\cdot \text{3}$

Simplify,

  $\text{100=3}p$ .

Divide each side by $\text{3}$ and simplify

  $\text{33}\text{.33=}p$

3. Consider the fraction $\frac{3}{8}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $\text{3 for }a\text{ and 8 for }b$ ,

  $\frac{3}{8}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 3=p\cdot 8$

Simplify,

  $300=8p$ .

Divide each side by $8$ and simplify

  $\text{37}\text{.5=}p$

4. Consider the fraction $\frac{5}{8}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $\text{5 for }a\text{ and 8 for }b$ ,

  $\frac{5}{8}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 5=p\cdot \text{8}$

Simplify,

  $500=8p$ .

Divide each side by $8$ and simplify

  $\text{62}\text{.5=}p$

5.Consider the fraction $\frac{2}{3}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $\text{2 for }a\text{ and 3 for }b$ ,

  $\frac{2}{3}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 2=p\cdot 3$

Simplify,

  $200=3p$ .

Divide each side by $\text{3}$ and simplify

  $\text{66}\text{.67=}p$

6. Consider the fraction $\frac{7}{8}$ ,

Write the proportion

  $\frac{a}{b}=\frac{p}{100}$

Substitute $\text{7 for }a\text{ and 8 for }b$ ,

  $\frac{7}{8}=\frac{p}{100}$

Use cross multiplication property

  $100\cdot 7=p\cdot 8$

Simplify,

  $700=8p$ .

Divide each side by $8$ and simplify

  $\text{87}\text{.5=}p$

Write the percents in tabular form: