Question

Insert 7 rational numbers between (5/6) and (7/9)

Answer 1

Answer:

84/108,85/108,86/108,87/108,88/108,89/108,90/108

Step-by-step explanation:

5/6*9/9=45/54

7/9*6/6=42/54

45/54*2/2=90/108

42/54*2/2=84/108

84/108,85/108,86/108,87/108,88/108,89/108,90/108

Answer 2

Seven rational numbers between 5/6 and 7/9 are 113/144, 114/144, 115/144, 116/144, 117/144, 118/144 and 119/144.

Rational numbers:

The numbers which are expressible in the form p/q, where p, q are integers with non-zero q, are called rational numbers.

For example, 2/3, 12/2, etc.

To find:

Seven rational numbers between 5/6 and 7/9

Step-by-step explanation:

The given two rational numbers are 5/6 and 7/9.

• Hint. First of all, we make the denominators of the rational numbers equal. Then increase denominators in such a way that it will be possible to insert seven or more rational numbers between them.

Here, LCM of 6 and 9 is 18.

Then,

• 5/6 = (5 × 3)/(6 × 3) = 15/18

• 7/9 = (7 × 2)/(9 × 2) = 14/18

• Hint. Now we increase the denominator by multiplying both the numerator and the denominator by 8.

So, we have

• 5/6 = 15/18 = (15 × 8)/(18 × 8) = 120/144

• 7/9 = 14/18 = (14 × 8)/(18 × 8) = 112/144

• Hint. Since both the denominators have the same number 144, we write seven rational numbers between 112/144 and 120/144.

Thus the required rational numbers are

113/144, 114/144, 115/144, 116/144, 117/144, 118/144 and 119/144.

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