Question

find six rational numbers between 3/4 and 4/5.

Answer 1

Let's make their denominators same firstly :



$\frac{3}{4} \times \frac{5}{5} = \frac{15}{20}$


And

$\frac{4}{5} \times \frac{4}{4} = \frac{16}{20}$


Now , Multiply both numbers by 10 [Both Denominator and Numerator]

= 150/200 and 160/200

6 Rational Numbers =

151/200, 152/200 , 153/200 , 154/200 , 155/200 , 156/200 .

[Note : There are infinite rational numbers between any 2 numbers]

Answer 2

Answer:

 $\frac{136}{180},\frac{137}{180},\frac{138}{180},\frac{139}{180}, \frac{140}{180},\frac{141}{180}.$

Step-by-step explanation:

Given: $\frac{3}{4}$ and $\frac{4}{5}$.

To find: Six rational number in between.

For this we'll multiply numerator & denominators by such a number that denominator became equal & at least six numbers falls between $\frac{3}{4}$ and $\frac{4}{5}$.

To make denominator equal take LCM$(4,5)=20$.

So, $\frac{3}{4}=\frac{3*5}{4*5} =\frac{15}{20}$

$\frac{4}{5} =\frac{4*4}{5*4}=\frac{16}{20}$

Now  to insert at least six numbers between $\frac{3}{4}$ and $\frac{4}{5}$ multiply numerator & denominator in $\frac{15}{20}$ & $\frac{16}{20}$ by 9.

$\frac{15*9}{20*9}=\frac{135}{180}$ and $\frac{16*9}{20*9}=\frac{144}{180}$

So, six number between $\frac{3}{4}$ and $\frac{4}{5}$ are: $\frac{136}{180},\frac{137}{180},\frac{138}{180},\frac{139}{180}, \frac{140}{180},\frac{141}{180}.$

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