Addition of Fractions

1. Addition of Fractions

2. Addition of Similar Fractions
𝟏𝟎
𝟐𝟕
+
𝟖
𝟐𝟕
=
𝟏𝟖
𝟐𝟕
Step 1: If the fractions are similar, just add the numerators and
Rewrite the denominator.

3. Addition of Similar Fractions
Step 2: Simplify the sum if possible.
𝟏𝟎
𝟐𝟕
+
𝟖
𝟐𝟕
=
𝟏𝟖
𝟐𝟕
=
𝟐
𝟑
=
𝟐 𝒙 𝟑 𝒙 𝟑
𝟑 𝒙 𝟑 𝒙 𝟑

4. Addition of Similar Fractions
Step 1: If the fractions are similar, just add the numerators and
Rewrite the denominator.
𝟏𝟓
𝟑𝟓
+
𝟏𝟎
𝟑𝟓
=
𝟐𝟓
𝟑𝟓

5. Addition of Similar Fractions
Step 2: Simplify the sum if possible.
𝟏𝟓
𝟑𝟓
+
𝟏𝟎
𝟑𝟓
=
𝟐𝟓
𝟑𝟓
=
𝟓
𝟕
=
𝟓 𝒙 𝟓
𝟓 𝒙 𝟕

7. Addition of
Dissimilar Fractions

8. Addition of Dissimilar Fractions
Step 1: Find the LCD of the given fractions.
𝟓
𝟖
+
𝟑
𝟔
8 = 2 x 2 x 2
6 = 2 x 3
LCD = 2 x 2 x 2 x 3
= 24

9. Addition of Dissimilar Fractions
Step 2: Change dissimilar fractions to similar fractions.
𝟓
𝟖
+
𝟑
𝟔
=
𝟏𝟓
𝟐𝟒
=
𝟏𝟐
𝟐𝟒

10. Addition of Dissimilar Fractions
Step 3: Add the numerators and copy the denominator.
𝟓
𝟖
+
𝟑
𝟔
=
𝟏𝟓
𝟐𝟒
=
𝟏𝟐
𝟐𝟒
𝟐𝟕
𝟐𝟒

11. Addition of Dissimilar Fractions
Step 4: If the answer is an improper fraction, change this to
a mixed number.
𝟓
𝟖
+
𝟑
𝟔
=
𝟏𝟓
𝟐𝟒
=
𝟏𝟐
𝟐𝟒
𝟐𝟕
𝟐𝟒
= 𝟏
𝟑
𝟐𝟒

12. Addition of Dissimilar Fractions
Step 5: Express the answer in its lowest term if needed .
𝟓
𝟖
+
𝟑
𝟔
=
𝟏𝟓
𝟐𝟒
=
𝟏𝟐
𝟐𝟒
𝟐𝟕
𝟐𝟒
= 𝟏
𝟑
𝟐𝟒
𝟏
𝟑
𝟐 𝒙 𝟐 𝒙 𝟐 𝒙 𝟑
= = 𝟏
𝟏
𝟖

14. Addition of
Mixed Numbers

15. Addition of Mixed Numbers
Step 1: Find the LCD of the given fractions.
𝟏
𝟓
𝟗
+ 𝟑
𝟏𝟎
𝟏𝟖
18 = 2 x 3 x 3
9 = 3 x 3
LCD = 2 x 3 x 3
= 18

16. Addition of Mixed Numbers
Step 2: Change dissimilar fractions to similar fractions.
+
𝟏
𝟓
𝟗
𝟑
𝟏𝟎
𝟏𝟖
=
=
𝟏
𝟏𝟎
𝟏𝟖
𝟑
𝟏𝟎
𝟏𝟖

17. Addition of Mixed Numbers
Step 3: Add the whole numbers and the numerators
and copy the denominator.
+
𝟏
𝟓
𝟗
𝟑
𝟏𝟎
𝟏𝟖
=
=
𝟏
𝟏𝟎
𝟏𝟖
𝟑
𝟏𝟎
𝟏𝟖
𝟒
𝟐𝟎
𝟏𝟖
+

18. Addition of Mixed Numbers
Step 4: If the answer is an improper fraction, change this to
a mixed number.
+
𝟏
𝟓
𝟗
𝟑
𝟏𝟎
𝟏𝟖
=
=
𝟏
𝟏𝟎
𝟏𝟖
𝟑
𝟏𝟎
𝟏𝟖
𝟒
𝟐𝟎
𝟏𝟖
+
= 𝟒 + 𝟏
𝟐
𝟏𝟖
𝟓
𝟐
𝟏𝟖
=

19. Addition of Mixed Numbers
Step 5: Express the answer in its lowest term if needed .
𝟏
𝟓
𝟗
𝟑
𝟏𝟎
𝟏𝟖
=
=
𝟏
𝟏𝟎
𝟏𝟖
𝟑
𝟏𝟎
𝟏𝟖
𝟒
𝟐𝟎
𝟏𝟖
+
=𝟓
𝟐
𝟏𝟖
+
= 𝟓
𝟐
𝟐 𝒙 𝟑 𝒙 𝟑
= 𝟓
𝟏
𝟗