Question

find ten rational number between. 3/5 and 3/4. please explain and answer because my exam tomorrow.​

Answer 1

To Find :

• Ten rational numbers between 3/5 and 3/4.

Solution :

In this question, we have to find ten rational numbers between 3/5 and 3/4. So firstly we will take the LCM (Lowest Common Factor) of the denominators to make the fraction same. After that we will find ten rational numbers between 3/5 and 3/4.

LCM of the denominators :

• LCM of the denominators = 2 | 4 , 5
• LCM of the denominators = 2 | 2 , 5
• LCM of the denominators = 5 | 1 , 5
• LCM of the denominators = | 1 , 1
• LCM of the denominators = 2 × 2 × 5 = 4 × 5 = 20

Making the Fraction same :

• 3/5 = 3 × 4/5 × 4 = 12/20
• 3/4 = 3 × 5/4 × 5 = 15/20

As we can see that there are only 3 rational numbers between 12/20 and 15/20, So we will replace numbers 12/20 and 15/20 by equivalent rational numbers having sufficiently large common denominator.

• 12/20 = 120/200
• 15/20 = 150/200

Now we can see that there are 30 rational numbers between 120/200 and 150/200 so we can write any ten.

Therefore :

• Ten rational numbers between 3/5 and 3/4 are 125/200 , 127/200 , 129/200 , 131/200 , 133/200 , 134/200 , 137/200 , 141/200 , 144/200 and 148/200.

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