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Find the reciprocal of the rational number (1/2)² ÷ (2/3)³

Solution:

Given, the expression is (1/2)² ÷ (2/3)³.

We have to find the reciprocal of the rational number.

Considering (1/2)²,

(1/2)² = (1 × 1)/(2 × 2)

= 1/4

Considering (2/3)³,

(2/3)³ = (2 × 2 × 2)/(3 × 3 × 3)

= 8/27

Now, (1/2)² ÷ (2/3)³ = (1/4) ÷ (8/27)

= (1/4) × (27/8)

= (1 × 27)/(4 × 8)

Number, n = 27/32

Reciprocal can simply be defined as the inverse of a number or a value.

For a real number n, reciprocal is 1/n

Reciprocal = 1/(27/32)

= 32/27

Therefore, the required value is 32/27.

✦ Try This: Find the reciprocal of the rational number (2/3)² ÷ (2/9)³

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 71

Summary:

The reciprocal of the rational number (1/2)² ÷ (2/3)³ is 32/27

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