This publication discusses what are reciprocal and reciprocal numbers. We also give a rule by which they can be found, and a practical example is analyzed for a better understanding of the theoretical material.
Content
Definition of reciprocals
Let’s say we have an ordinary fraction
3/7
.
If we swap the numerator and denominator in places (i.e., “turn over” the fraction), we get
7/3
.
Fraction
7/3
called inverse fractions
3/7
.
Also, if we flip
7/3
, then you get the original fraction
3/7
.
Consequently, the
3/7
и
7/3
are reciprocal numbers.
Note: the product of mutually reciprocal numbers is equal to one.
a ·
1/a
= 1
For example:
9/XNUMX/XNUMX
1/9
= 1
2/11
·
11/2
= 1
The rule for finding the reciprocal
- We represent the original number (whole or mixed) as an ordinary fraction.
- Reverse the resulting fraction.
Example
Find the reciprocal of the mixed fraction 3
4/5
.
Decision:
First, let’s convert the fraction to a common fraction:
3
4/5
=
3 5 + 4/5
=
19/5
Swapping the numerator and denominator, we get the reciprocal of the number equal to
5/19
.