Question

Find six rational numbers between
i) -3/2 and 5/3
ii) 2/3 and 4/5


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Answer 1

Answer:

Step-by-step explanation:

1) -3/2 and 5/3

Find LCM of the denominators 2 and 3, which is 6.

Multiply -3/2 with 3 on both denominator and numerator and the product will be -9/6.

Multiply 5/3 with 2 on both numerator and denominator, the product will be 10/6.

Therefore, you can select any six rationals between -9/6 and 10/6

For example: -8/6,  -7/6,  -5/6,  -4/6,  -3/6 and -2/6

2)  2/3 and 4/5

LCM = 15. Multiply and make the denominators 15 using appropriate numbers.

Here: 2/3 should be multiplied by 5 on both numerator and denominator to get 10/15 and the other will be 20/15.

Here, as there are only 15 numbers between them, we can multiply 10 to both the numerator and denominator of both the rational number.

We get: 100/150 and 200/150.(It isn't necessary to multiply with 10, you can multiply with any other number except 0 and 1)

As we get 100/150 and 200/150, we get 100 numbers between them, you can select any 6.

For example: 101/150,  102/150,  103/150, 104/150, 105/150 and 106/150

Answer 2

1) -3/2 and 5/3

Find LCM of the denominators 2 and 3, which is 6.

Multiply -3/2 with 3 on both denominator and numerator and the product will be -9/6.

Multiply 5/3 with 2 on both numerator and denominator, the product will be 10/6.

Therefore, you can select any six rationals between -9/6 and 10/6

For example: -8/6, -7/6, -5/6, -4/6, -3/6 and -2/6

2) 2/3 and 4/5

LCM = 15. Multiply and make the denominators 15 using appropriate numbers.

Here: 2/3 should be multiplied by 5 on both numerator and denominator to get 10/15 and the other will be 20/15.

Here, as there are only 15 numbers between them, we can multiply 10 to both the numerator and denominator of both the rational number.

We get: 100/150 and 200/150.(It isn't necessary to multiply with 10, you can multiply with any other number except 0 and 1)

As we get 100/150 and 200/150, we get 100 numbers between them, you can select any 6.

For example: 101/150, 102/150, 103/150, 104/150, 105/150 and 106/150

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