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.
\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 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.
\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 equivalent and add the fractions with like denominator.
\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 numbers 3 + 2 = 5 step 2: Add the fractions: Find the LCD of the denominators 3 and 7, write equivalent fractions with common denominator 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 whole number obtained in step 1 and the mixed number obtained in step 3
5 + 1 \dfrac{8}{21} = 6\dfrac{8}{21}
Questions with answers: Add and reduce if possible the following fractions and mixed numbers. 1.
\dfrac{1}{5} + \dfrac{3}{5}
2.
\dfrac{3}{5} + \dfrac{4}{7}
3.
7 \dfrac{3}{5} + 3
4.
4 \dfrac{2}{3} + 2 \dfrac{9}{11}

2.