Contents
In this publication, we will look at how you can add ordinary (simple) fractions with the same / different denominators and mixed fractions. We will also analyze examples of solving problems for a better understanding and consolidation of theoretical material.
Addition of fractions
With the same denominators
In this case, everything is extremely simple. When adding fractions with the same denominators, the numerators are added together, but the denominator remains the same.
+
=
Note: obtained by adding a new fraction in some cases, you can.
With different denominators
To add fractions with different denominators, follow these steps:
1. We bring the given fractions to .
2. We add the results as fractions with the same denominators.
Sum of mixed fractions
To add mixed fractions, you need to sum the whole parts separately, and separately the fractional parts.
+ Y
= (X + Y(+)
+
)
Note: If the fractional parts have different denominators, then they must first be brought to the lowest common denominator, and only then added.
Examples of tasks
Task 1
и
.
Solution
Because we have fractions with the same denominators, then:
+
=
=
=1
Task 2
и
.
Solution
In this case, we first need to reduce the fractions to the lowest common denominator.
both denominators is 84, therefore, the additional factor for the first fraction is the number 7, for the second – 12.
=
=
=
=
Thus, we got fractions with the same denominators, and now they can be added:
+
=
=
Task 3
and 5
.
Solution
The fractional parts have the same denominator, which means we can immediately perform the addition:
+ 5
= 2 + 5 + (
+
) = 7 +
= 7