## The Lesson

Improper fractions can be converted to mixed fractions. • An improper fraction (or top-heavy fraction) is a fraction where the top number is greater than (or equal to) the bottom number.
• A mixed fraction has a whole number and a fraction.

## Question

Convert the improper fraction below to a mixed fraction. # 1

Divide the top number (called the numerator) of the fraction by the bottom number (called the denominator). Express it as a quotient and a remainder.
5 ÷ 2 = 2 r 1
Don't forget: If a number does not divide exactly into another, you get a quotient (2 in our example) and a remainder (1) that is left over. r means remainder. See the Note.

# 2

Use the answer from Step 1...
2 r 1
to write the mixed fraction. Write the quotient (2) as the whole number part of the mixed fraction. # 3

Use the answer from Step 1...
2 r 1
to write the mixed fraction. Write the remainder (1) as the numerator of the fraction part of the mixed fraction. # 4

Find the denominator of the fraction.
2 1/?
The denominator of the original improper fraction (2) becomes the denominator of the fraction part of the mixed fraction. # 5

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).

2 1/2 (two and a half) is 5/2 (five-halves) written as a mixed fraction. ## Lesson Slides

The slider below shows another real example of converting improper fractions to mixed fractions.

## What Is a Remainder?

A number can often be divided exactly by another number. For example, 4 ÷ 2 = 2. This means 4 objects can be divided into 2 equal groups of 2: However, try 5 ÷ 2. There are 2 equal groups of 2, but 1 is left over: 5 ÷ 2 = 2 with a remainder 1

5 ÷ 2 = 2 r 1

2 is the quotient. 1 is the remainder.

## How to Find the Quotient and Remainder with a Calculator

This Note explains how to find Step 1 in our example.

## Question

Find 5 ÷ 2, expressing the answer as a quotient and a remainder.
Using the on-screen calculator:
• Type 5 ÷ 2. • Click the = button. The answer is 2.5. The number to the left of the decimal point (2 in our example) is the quotient. The quotient is 2. To find the remainder, start with 2.5 still showing in the calculator.
• Subtract the quotient. Type − 2. • Click the = button. The answer is 0.5. • Multiply by the number you first divided by (2 in this example, as we are finding 5 ÷ 2). Type × 2. • Click the = button. The answer is 1. This is the remainder. The remainder is 1.
5 ÷ 2 = 2 r 1.