Question
Find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}.$
✓
Answer
The $LCM$ of the denominators $5$ and $4$ of both the fraction is $20$.
We can write: $\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$ Since the intergers between the numerators $12$ and $15$ are not sufficient, we will multiply both the fraction by $5$.
$\frac{12}{20}=\frac{12\times5}{200\times5}=\frac{60}{100}$
$\frac{15}{20}=\frac{15\times5}{20\times5}=\frac{75}{100}$
There are $14$ integers between $60$ and $75$. They are $61, 62, 63,........... 73$ and $74$.
Therefore, $\frac{60}{100},\frac{61}{100},\frac{62}{100},...........\frac{73}{100}$ and $\frac{74}{100}$ are the $14$ fractions.
We can take any $10$ of these.
We can write: $\frac{3}{5}=\frac{3\times4}{5\times4}=\frac{12}{20}$
$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$ Since the intergers between the numerators $12$ and $15$ are not sufficient, we will multiply both the fraction by $5$.
$\frac{12}{20}=\frac{12\times5}{200\times5}=\frac{60}{100}$
$\frac{15}{20}=\frac{15\times5}{20\times5}=\frac{75}{100}$
There are $14$ integers between $60$ and $75$. They are $61, 62, 63,........... 73$ and $74$.
Therefore, $\frac{60}{100},\frac{61}{100},\frac{62}{100},...........\frac{73}{100}$ and $\frac{74}{100}$ are the $14$ fractions.
We can take any $10$ of these.
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