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If p/q is a rational number and m is a non-zero common divisor of p and q, then p/q = p ÷ m / q ÷ m. Is the given statement true or false?

Solution:

Given, if p/q is a rational number and m is a non-zero common divisor of p and q, then p/q = p ÷ m / q ÷ m

We have to determine if the given statement is true or false

If the numerator and denominator of a rational number is multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number.

Let m = 1

p ÷ m / q ÷ m = p ÷ (1) / q ÷ (1)

= (p/1) ÷ (q/1)

= (p/1) × (1/q)

= p/q

Let m = 2

p ÷ m / q ÷ m = p ÷ (2) / q ÷ (2)

= (p/2) ÷ (q/2)

= (p/2) × (2/q)

= p/q

Let m = 3

p ÷ m / q ÷ m = p ÷ (3) / q ÷ (3)

= (p/3) ÷ (q/3)

= (p/3) × (3/q)

= p/q

Therefore, it is true that p/q = p ÷ m / q ÷ m

✦ Try This: If p/q is a rational number and 4 is a non-zero common divisor of p and q, then p/q = p ÷ 4 / q ÷ 4. Is the given statement true or false?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 9

NCERT Exemplar Class 7 Maths Chapter 8 Problem 52

If p/q is a rational number and m is a non-zero common divisor of p and q, then p/q = p ÷ m / q ÷ m. Is the given statement true or false?

Summary:

The given statement, “If p/q is a rational number and m is a non-zero common divisor of p and q, then p/q = p ÷ m / q ÷ m” is true

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