Contents
In this publication, we will look at how you can find the difference between ordinary (simple) fractions with different or the same denominators, and how the subtraction of mixed fractions is performed. We will also analyze examples of solving problems for a better understanding and consolidation of theoretical material.
Subtraction of fractions
With the same denominators
When subtracting fractions with the same denominators, the numerator of the second fraction is subtracted from the numerator of the first fraction. The denominator remains the same.
–
=
Note: You should check the new fraction obtained by subtraction. Perhaps it can.
With different denominators
To subtract one fraction from another, the denominator of which is different from the first, we need:
1. Bring these fractions to .
2. Then perform the subtraction – as for fractions with the same denominators.
Difference of mixed fractions
To find the difference between mixed fractions, first subtract their whole parts separately, then the fractional parts separately. We add up the results.
– Y
= (X – Y(+)
–
)
Note: If the fractional parts have different denominators, we first reduce them to the lowest common denominator, then subtract them.
Examples of tasks
Task 1
и
.
Solution
These fractions have the same denominator, so:
–
=
=
Task 2
и
.
Solution
First, we reduce the fractions to the lowest common denominator.
both denominators equals 140. This means that the additional factor for the first fraction is 20, for the second – 7.
=
=
=
=
Now we have fractions with the same denominators, and we can subtract the second from the first:
–
=
=
Task 3
fraction 2
.
Solution
Since the fractional parts have the same denominators, we can immediately perform the subtraction:
– 2
= 3 – 2 + (
–
) = 1 +
= 1