Question

Find ten rational numbers between $\frac{3}{5}and\frac{3}{4}$.

• A. $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{80}{100}$.
• B. $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{70}{100}$.
• C. $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{90}{100}$.
• D. $\frac{41}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{70}{100}$.

Answer 1

The correct option is B $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{70}{100}$.

Converting the given rational numbers with the same denominators
$\frac{3}{5}=\frac{3\times 20}{5\times 20}=\frac{60}{100}and\frac{3}{4}=\frac{3\times 25}{4\times 25}=\frac{75}{100}$

We know that,
$60<61<62<63<\dots <72<73<74<75$
$\Rightarrow \frac{60}{100}<\frac{61}{100}<\frac{62}{100}<\frac{63}{100}<\dots <\frac{72}{100}<\frac{73}{100}<\frac{74}{100}<\frac{75}{100}$.

Thus, we have the following ten rational numbers between $\frac{3}{5}and\frac{3}{4}$
$\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100}and\frac{70}{100}$.