Reciprocal of a Fraction
Remember that a fraction has three parts.
Parts of a Fraction
Example 1: Find the reciprocal of the fraction .
Let’s turn the fraction upside down to get its reciprocal. This gives us .
Example 2: Find the reciprocal of the fraction .
This can be tricky to some. Notice that the numerator is negative. If we turn this fraction upside down, we should naturally get
Since this is a negative fraction, the negative symbol may not always “follow” the number that it is initially attached to.
In other words, the negative symbol can stay in the numerator. And so, after inverting the two numbers, the negative symbol is now attached to 2. This is also a valid answer as the reciprocal of the original fraction.
There is one more way to write the reciprocal of this negative fraction. The negative symbol may not be attached either to the numerator or denominator.
It is also correct to place the negative symbol directly to the left of the fraction bar. This is how it looks!
So in summary, if the fraction is negative its reciprocal can be written three ways.
- Negative symbol stays with the numerator
- Negative symbol stays with the denominator
- Negative symbol stays with the fractional bar
Example 3: Write the reciprocal of the negative fraction in three different ways.
Example 4: Find the reciprocal of the whole number 15.
Any nonzero whole number can be expressed with a denominator of 1.
By having a clear denominator, we can easily flip this fraction upside down to get its reciprocal.
Example 5: Find the reciprocal of the integer –11.
First, rewrite this integer with a denominator of 1 as well.
By having a distinct denominator, we can now find its reciprocal. We have a negative symbol on the numerator, remember that it can be positioned in three different places: numerator, denominator and by the fraction bar. Here are the possible answers!