Question

Find a rational number between 2/3 and 3/4 ( hint : first write the rational number with equal denominator

Answer 1

Answer:

8/12,9/12 are two rational numbers with same denominator

multiply these by 2/2

number will be 16/24,18/24

17/24 is the rational number

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Answer 2

Step-by-step explanation:

First we will take L.C.M of the given rationals :

$\frac{2}{3} and \frac{3}{4} \\ = lcm \: of \: 3 \: and \: 4 \: = 12 \\ \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \\ \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

Then we get the rationals with equal denominators :

• 8/12
• 9/12

Now we will multiply both the rationals with any number .Here we will take 10 for example to expand them :

$\sf{ \frac{8 \times 10}{12 \times 10} = \frac{80}{120} \\ = \frac{9 \times 10}{12 \times 10} = \frac{90}{120}$

Now we can take any number between 80/120 and 90/120.

Eg :

• 81/120
• 82/120
• 83/120
• 84/120
• 85/120
• 86/120
• 87/120
• 88/120
• 89/120