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 = 12 × 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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