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. More resources on fractions are included.

Examples with Solutions

Example 1: Add fractions with like (same) denominators

\[ \dfrac{1}{4} + \dfrac{2}{4} \]

Solution to example 1:

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

\[ \dfrac{1}{4} + \dfrac{2}{4} = \dfrac{1+2}{4} = \dfrac{3}{4} \]

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

\[ \dfrac{4}{7} + \dfrac{2}{5} \]

Solution to example 2:

  • Step 1: Find the lowest common multiple (LCM) of the denominators 7 and 5.
    Multiples of 7 are: 7, 14, 21, 28, 35, 42, ...
    Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...
    The lowest common multiple (LCM) of 7 and 5 is 35, making the lowest common denominator (LCD) equal to 35.
  • Step 2: Write equivalent fractions with a lowest common denominator (LCD) equal to the LCM.
    \[ \dfrac{4}{7} = \dfrac{4 \times \color{red}{5}}{7 \times \color{red}{5}} = \dfrac{20}{35} \] and \[ \dfrac{2}{5} = \dfrac{2 \times \color{red}{7}}{5 \times \color{red}{7}} = \dfrac{14}{35} \]
  • Step 3: Replace the given fractions by their equivalents and add the fractions with like denominators.
    \[ \dfrac{4}{7} + \dfrac{2}{5} = \dfrac{20}{35} + \dfrac{14}{35} = \dfrac{34}{35} \]
  • Step 4: Reduce the fraction if possible.
    The fraction obtained above cannot be further reduced.

Example 3: Add the mixed numbers.

\[ 3 \dfrac{2}{3} + 2 \dfrac{5}{7} \]

Solution to example 3:

  • Step 1: Add the whole parts of the mixed numbers: \(3 + 2 = 5\)
  • Step 2: Add the fractions: Find the LCD of the fractions with denominators 3 and 7.
    Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, ...
    Multiples of 7 are: 7, 14, 21, 28, 35, 42, ...
    The LCD is 21 (the LCM of 3 and 7).
    Write equivalent fractions with LCD and add the fractions.
    \[ \dfrac{2}{3} + \dfrac{5}{7} = \dfrac{14}{21} + \dfrac{15}{21} = \dfrac{29}{21} \]
  • Step 3: Reduce and write the fraction as a mixed number if possible.
    \[ \dfrac{29}{21} = \dfrac{21+8}{21} = \dfrac{21}{21} + \dfrac{8}{21} = 1 \dfrac{8}{21} \]
  • Step 4: Add the sum of the whole parts obtained in step 1 and the mixed number obtained in step 3.
    \[ 5 + 1 \dfrac{8}{21} = 6\dfrac{8}{21} \]

Questions and Step-by-Step Solutions

Add and reduce if possible the following fractions and mixed numbers.

  1. Question 1:
    \( \dfrac{1}{5} + \dfrac{3}{5} \)

    View Step-by-Step Solution

    Explanation:

    Both fractions have the same denominator (5). Add the numerators: \(1 + 3 = 4\).

    Answer: \(\dfrac{4}{5}\)

  2. Question 2:
    \( \dfrac{3}{5} + \dfrac{4}{7} \)

    View Step-by-Step Solution

    Explanation:

    • Find the LCD for denominators 5 and 7, which is \(35\).
    • Convert fractions: \(\dfrac{3}{5} = \dfrac{21}{35}\) and \(\dfrac{4}{7} = \dfrac{20}{35}\).
    • Add: \(\dfrac{21}{35} + \dfrac{20}{35} = \dfrac{41}{35}\).
    • Convert to a mixed number: \(\dfrac{41}{35} = 1 \dfrac{6}{35}\).

    Answer: \(1 \dfrac{6}{35}\)

  3. Question 3:
    \( 7 \dfrac{3}{5} + 3 \)

    View Step-by-Step Solution

    Explanation:

    Add the whole numbers: \(7 + 3 = 10\). Keep the fractional part \(\dfrac{3}{5}\).

    Answer: \(10 \dfrac{3}{5}\)

  4. Question 4:
    \( 4 \dfrac{2}{3} + 2 \dfrac{9}{11} \)

    View Step-by-Step Solution

    Explanation:

    • Add the whole parts: \(4 + 2 = 6\).
    • Find the LCD for fractions with denominators 3 and 11, which is \(33\).
    • Convert fractions: \(\dfrac{2}{3} = \dfrac{22}{33}\) and \(\dfrac{9}{11} = \dfrac{27}{33}\).
    • Add fractions: \(\dfrac{22}{33} + \dfrac{27}{33} = \dfrac{49}{33} = 1 \dfrac{16}{33}\).
    • Combine with whole parts: \(6 + 1 \dfrac{16}{33} = 7 \dfrac{16}{33}\).

    Answer: \(7 \dfrac{16}{33}\)

More References and Links