Question

Evaluate . Express as in rational number in its lowest form.
(a) 7/16+-8/13+-9/8+21/3
(b) 7/16+-6/11+-8/9+7/11

Answer 1

We will learn the reciprocal of a rational number.

For every non-zero rational number a/b there exists a rational number b/a such that

a/b × b/a = 1 = b/a × a/b

The rational number b/a is called the multiplicative inverse or reciprocal of a/b and is denoted by (a/b)-1.

The reciprocal of 12 is 1/12

The reciprocal of 5/16 is 16/5.

The reciprocal of 3/4 is 4/3 i.e., (3/4)^-1 = 4/3.

The reciprocal of -5/12 is 12/-5 i.e., (-5/12)^-1 = 12/-5.

The reciprocal of (-14)/17 is 17/-14 i.e., (-17)/14.

The reciprocal of -8 is 1/-8 i.e., (-1)/8.

The reciprocal of -5 is 1/-5, since -5 × 1/-5 = -5/1 × 1/-5 = -5 × 1/-5 × 1 = 1.

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