Question

find three rational number between

Answer 1

(a) 11/16 ≤ 17/24 ≤ 35/48
(b) 3/8 ≤ 5/12 ≤ 11/24
(c) 3.25 ≤ 3.59 ≤ 3.75
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Answer 2

Answer:

1. 33/48, 34/48, 35/48    2. 9/24, 10/24, 11/24     3. 13/4, 14/4, 15/4

Step-by-step explanation:

1. We need to find 3 rational numbers between 2/ 3 and 3/4. LCM is 12. Since it is 3 rational numbers we can take the next number as 4. Multiply and divide these fraction by 4 and 3 we get

2/3 x 4/4 = 8 / 12

3/4 x 3/3 = 9/12

Now we can multiply and divide by 4 we get

8/12 x 4/4 = 32/48  and 9/12 x 4/4 = 36/48

The larger the denominator we get more number of fractions between them.

We get 3 fractions that is 33/48 , 34/48 and 35/48

2. We need to find 3 rational numbers between 1/ 3 and 1/2. LCM is 6. Since it is 3 rational numbers we can take the next number as 4. Multiply and divide these fraction by 2 and 3 we get

1/3 x 2/2 = 2 / 6

1/2 x 3/3 = 3/6

Now we can multiply and divide by 4 we get

2/6 x 4/4 = 8/24  and 3/6 x 4/4 = 12/24

The larger the denominator we get more number of fractions between them.

We get 3 fractions that is 9/24 , 10/24 and 11/24

3. We need to find 3 rational numbers between 3/ 1 and 4/1. LCM is 1. Since it is 3 rational numbers we can take the next number as 4. Multiply and divide these fraction by 4 we get

3/1 x 4/4 = 12 / 4

4/1 x 4/4 = 16/4

We get 3 fractions that is 13/4 , 14/4 and 15/4