Question 52 State whether the given statement is True or False- If p - j is a rational number and m is a non-zero common divisor of p and q- then p - q - p - m - q - m-

Name: EXEMP - Grade 07 - Mathematics - Rationals Numbers - Q52
Uploaded: 2022-07-04T10:36:42+05:30
Description: True Example: Let m = 1, 2, 3 ..... When m = 1 thenp/q = p ÷ 1/q ÷ 1 = p/1÷q/1 = p/1×1/q = p/q When m = 2 then p/q = p ÷ 2/ q ÷ 2 = p/2÷q/2 = p/2×2/q = p/q Henc ...

True Example: Let m = 1, 2, 3 ..... When m = 1 thenp/q = p ÷ 1/q ÷ 1 = p/1÷q/1 = p/1×1/q = p/q When m = 2 then p/q = p ÷ 2/ q ÷ 2 = p/2÷q/2 = p/2×2/q = p/q Henc ...

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Byju's Answer

Standard VII

Mathematics

Rational Numbers

Question 52 S...

Question

Question 52

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero common divisor of p and q, then $\frac{p}{q} = \frac{p \div m}{q \div m} .$

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Solution

True

Example: Let m = 1, 2, 3 .....
When m = 1 then $\frac{p}{q} = \frac{p \div 1}{q \div 1} = \frac{p}{1} \div \frac{q}{1} = \frac{p}{1} \times \frac{1}{q} = \frac{p}{q}$
When m = 2 then $\frac{p}{q} = \frac{p \div 2}{q \div 2} = \frac{p}{2} \div \frac{q}{2} = \frac{p}{2} \times \frac{2}{q} = \frac{p}{q}$
Hence, $\frac{p}{q} = \frac{p \div m}{q \div m}$

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Question 51

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero integer then $\frac{p}{q} = \frac{p \times m}{q \times m}$

Question 54

State whether the given statement is True or False.

If $\frac{p}{q}$ is a rational number and m is a non-zero integer, then $\frac{p \times m}{q \times m}$ is a rational number not equivalent to $\frac{p}{q}$ .