Addition of proper fraction and improper fraction is solved with the same method as in the addition of proper fractions.
In this lesson, you will learn the step-by-step method for the addition of proper fraction and improper fraction.
BONUS: A link to practice questions on fractions is included at the end of this lesson.
Question on addition of proper fraction and improper fraction
Let’s take an example:
Question:
What is the sum of
\dfrac{1}{6} and \dfrac{7}{3}
STEP 1.
Find the LCM of the denominators
Workings:
The LCM of the denominators 6 and 3
= 6
STEP 2.
Write the LCM as your new single denominator
\frac{}{6}STEP 3.
Divide the LCM by each of the original denominators
Workings:
6 ÷ 6 = 1
6 ÷ 3 = 2
STEP 4.
Multiply your STEP 3. answers with their numerators.
Workings:
1 × 1 = 1
2 × 7 = 14
STEP 5.
Write your STEP 4. answers as the new numerators
\dfrac{1+14}{6}STEP 6.
Add your new numerators, and leave the LCM as it is
= \dfrac{15}{6}STEP 7.
Reduce your answer to a fraction in its lowest term.
= \frac{5}{2}Final answer
The addition of proper fraction and improper fraction in the question
\dfrac{1}{6} and \dfrac{7}{3}
= \dfrac{5}{2}
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