i have learned that if a, b and c denote integers and b#0 then a/b + c/b = ___ i also knew that every rational number expect ___ has a unique reciprocal. so, the reciprocal of 5/4 is ___ fraction having the same denominator are called ___ while a fraction containing a whole number and a fraction is called ___ . i realize that to add subtract decimal arrange the digit in ___ according to their ___ to multiply decimal, multiply the numbers and count the total number of ___ in the fraction to divide decimal, multiply both the ___ and the ___ on the same multiple of 10 to make the divisor a whole number
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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. The reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1 and -1 are the only rational numbers which are their own reciprocals. No other rational number is its own reciprocal.
We know that there is no rational number which when multiplied with 0, gives 1. Therefore, rational number 0 has no reciprocal or multiplicative inverse.
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