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Write four rational numbers between $\frac{3}{4}$ and $\frac{2}{ 3}$.
Given: The two rational number are $\frac{3}{4}$ and $\frac{2}{ 3}$
To do: Find fours rational number between teh two given rational numbers.
Solution:
To solve this question, first we need to find LCM of the denominators and convert them into like fractions.
LCM of denominators 3 and 4 is 12.
To convert into like fractions we will multiply numerator and denominator of $\frac{3}{4}$ with 3. Similarly we will multiply numerator and denominator of $\frac{2}{3}$ with 4
$\frac{3}{ 4} = \frac{3}{4}\times\frac{3}{3} = \frac{9}{12}$
$\frac{2}{3} = \frac{2}{3}\times\frac{4}{4} = \frac{8}{1}$
Now our numbers are $\frac{8}{12}$ and $\frac{9}{12}$.
Now in between the numerators 8 and 9, there are no integers.
So we have to multiply both the numbers numerator and denominator again to see that there are sufficient numbers.
Let us multiply both the numbers numerator and denominator with 5.
$\frac{8}{12} \times \frac{5}{5} = \frac{40}{60}$.
$\frac{9}{12}\times\frac{5}{5}=\frac{45}{60}$.
So, the two numbers are $\frac{40}{60}$and $\frac{45}{60}$.
Now we find 4 Rational Numbers between them as $\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60}$.
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