Equivalent rational numbers

Equivalent rational numbers

We know how to write equivalent fractions when a fraction is given. Since a rational number can be represented by a fraction, we can think of equivalent rational numbers, duly obtained through equivalent fractions.

Suppose a rational number is in fractional form. Multiply its numerator and denominator by the same non-zero integer to obtain a rational number which is equivalent to it.

For example,

1. 7/3 = ?/9 = 49/? = −21/?

7/3 = [7 × 3] / [3 × 3] = 21 / 9

7/3 = [7 × 7] = [3 × 7] = 49 / 21

7 / 3 = [7 × (−3)] / [3 × (−3)] = −21 / −9

∴ 7/3 = 21/9 = 49/21 = −21/−9

2. −2 / 5 = ? / 10 = 6 / ? = −8 / ?

−2 / 5  = [−2 × 2] / [5 × 2] = −4 / 10

−2 / 5 = [−2 ×  −3] / [ 5 × −3] = 6 / −15

−2 / 5 = [−2 ×  4] / [5 ×  4] = −8 / 20

∴  −2 / 5 = [−4 / 10] = 6 / −15 = −8 / 20