The reciprocal or multiplicative inverse of a number x is the number which, when multiplied by x, gives 1. So, the product of a number and its reciprocal is always 1. This is sometimes called the property of reciprocals. Note that the number 0 has no reciprocal.
In mathematics, the reciprocal of any number is one divided by that number. For any number n, the reciprocal will be . If the given number is multiplied by its reciprocal, we get the value 1.
Example 1
The reciprocal of 7 is , which we can show by multiplying 7 and
Other definitions of reciprocals:
The reciprocal of a number is defined as one over that number.
Example 2
The reciprocal of 5 is because .
For any negative number , the reciprocal can be found by writing the inverse of the given number with a minus sign along with that.
Example 3
The reciprocal of is .
The reciprocal of a fraction can be found by interchanging the values of the numerator and denominator.
Example 4
The reciprocal of is .
In order to find a reciprocal for a mixed fraction, first convert it into an improper fraction and perform the operation.
Example 5
Find the reciprocal of the mixed fraction .
The first step is to convert the mixed fraction into an improper fraction.
Now you perform the same operation to find the reciprocal by flipping the numerator and denominator.
The reciprocal for is .
So the reciprocal for is .
The reciprocal of a decimal is the same as it is for the reciprocal of a number defined by one over the number.
Example 6
The reciprocal of a number .
So, the reciprocal of the decimal .
One of the main applications of reciprocal numbers is in the division of fractions. To divide the first fraction by the second fraction, the result can be found by multiplying the first fraction with the reciprocal of the second fraction.
Example 7
divided by
The reciprocal of the second fraction is .
So divided by
The answer to divided by is .
The two most important rules for reciprocals are:
Common Core: 6th Grade Math Flashcards
MAP 6th Grade Math Practice Tests
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