Addition Of Proper Fraction And Improper Fraction

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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