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Answer:
Properties of rational number are
(1) two rational numbers p/q and r/s are said to be equivalent if p×s=r×q
For example - to show 4/-7 and 8/-14 are equivalent rational numbers
Solution 4×(-14) = -56= 8×(-7) [by cross multiple] hence 4/-7 and 8/-14 are equivalent rational numbers.
(2) if p/q is rational number and m be integer different from 0 ,then p/q=p×m/q×m
For example - write three rational numbers which are equivalent to 3/5
Solution - to find equivalent rational number, multiple numerator and denominator by any non zero integer.
3×2/5×2= 6/10
3×(-3)/5×(-3)= -9/-15
3×5/5×5= 15/25
So the required number which are equivalent to 3/5 are 6/10 , -9/-15 , 15/25.
(3) if p/q is rational number and m is common divisor of p and q then p/q= p÷m/q÷m
For example - express -21/49 as a rational number with denominator 7
Solution to get denominator 7 , we must divide 49/7
Therefore , -21÷7/49÷7= -3/7
So required number is -3/7
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