Chapter 2.3, Problem 47E

To determine

ToCompare:The numbers $60\%$ and $\frac{2}{3}$ . And identify which number is greater.

Answer to Problem 47E

  $\frac{2}{3}$ is greater than $60\%$

Explanation of Solution

Given:

The numbers $60\%$ and $\frac{2}{3}$

Concept Used:

To convert a percentage into fraction, divide the number by $100$ and remove the percentage sign.

For like fractions, the fraction with greater numerator is the greater fraction.

Calculation:

Given the numbers $60\%$ and $\frac{2}{3}$

Converting $60\%$ into fraction

  $\begin{array}{c}60\%=\frac{60}{100}\\ =\frac{60÷20}{100÷20}\text{ Divide numerator and denominator by 2}0\\ =\frac{3}{5}\text{ Simplify}\\ =\frac{3\times 3}{5\times 3}\text{ Multiply numerator and denominator by 3}\end{array}$

  $=\frac{9}{15}\text{ Simplify}$

Converting $\frac{2}{3}$ into equivalent fraction

  $\begin{array}{c}\frac{2}{3}=\frac{2\times 5}{3\times 5}\text{ Multiply numerator and denominator by }5\\ =\frac{10}{15}\text{ Simplify}\end{array}$

Since, $\frac{10}{15}$ and $\frac{9}{15}$ are like fractions.

So, $\frac{10}{15}>\frac{9}{15}$

Since, $\frac{2}{3}=\frac{10}{15}$ and $60\%=\frac{9}{15}$

Therefore, $\frac{2}{3}>60\%$

Conclusion:

  $\frac{2}{3}$ is greater than $60\%$