Add Fractions and Mixed Numbers - Examples and Questions with Answers (Grade 5)

Grade 5 questions on how to add fractions and mixed numbers with answers are presented. Both fractions with like and unlike denominators are considered and the use of the lowest common denominator (LCD) is demonstrated.




Example 1:  Add fractions with like (same) denominators
  1   2
Add the fractions ____ + ____
  4   4

Solution to example 1:

When the fractions have the same denominator, we add the numerators and keep the same denominator

1   2   3
____ + ____ = ____
4   4   4



Example 2:  Add fractions with unlike (different) denominators.

  4   2
Add the fractions ____ + ____
  7   5

Solution to example 2:

step 1: Find the lowest common multiple (LCM) of the two denominators.

The LCM of 7 and 5 is 35.

step 2: Write equivalent fractions with a lowest common denominator (LCD) equal to the LCM.

4   4 x 5   20
____ = ____ = ____
7   7 x 5   35

and

2   2 x 7   14
____ = ____ = ____
5   5 x 7   35

step 3: Replace the given fractions by their equivalent and add the fractions with like denominator.

4   2   20   14   34
____ + ____ = ____ + ____ = ____
7   5   35   35   35


step 3: Reduce the fraction if possible.

The fraction obtained above cannot be further reduced.



Example 3:  Add fractions mixed numbers.

    2     5
Add the mixed numbers 3 ____ + 2 ____
    3     7

Solution to example 3:

step 1: Add the whole numbers   3  + 2 = 5

step 2: Find the LCD, equivalent fractions with common denominator and add the fractions.

2   5   14   15   29
____ + ____ = ____ + ____ = ____
3   7   21   21   21

step 3: Reduce and write the fraction as a mixed number if possible.

29     8
____ = 1 ____
21     21

step 4: Add the whole number obtained in step 1 and the mixed number obtained in step 3

      8     8
5 + 1 ____ = 6 ____
      21     21



Questions with answers: Add and reduce if possible the following fractions and mixed numbers.

1.
1   3
______ + ______
5   5
2.
3   4
______ + ______
5   7
3.
3    
7 ______ + 3
5    
4.
2     9
4 ______ + 2 ______
3     11

Answers to above questions

1.
4
______
5
2.
  6
1 ______
  31
3.
  3
10 ______
  5
4.
  16
7 ______
  33


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Updated: 14 March 2009 (A Dendane)