# How to Convert from Improper Fractions to Mixed Fractions (Mathematics Lesson)

# Converting from Improper to Mixed Fractions

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.

# How to Convert from Improper to Mixed Fractions

#### An Example Question

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

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**.

Step 2

**Step 1**) is used to write the mixed fraction.

Write the quotient (2) as the whole number part of the mixed fraction.

Step 3

**Step 1**) is used to write the mixed fraction.

Write the remainder (1) as the numerator of the fraction part of the mixed fraction.

Step 4

2

The denominator of the original improper fraction (2) becomes the denominator of the fraction part of the mixed fraction.^{1}/_{?}Step 5

2

^{1}/

_{2}(two and a half) is

^{5}/

_{2}(five-halves) written as a mixed fraction.

# A Real Example of How to Convert from Improper to Mixed Fractions

The slider below shows another example of converting improper fractions to mixed fractions:##### Interactive Test

**show**

Here's a second test on converting improper fractions to mixed fractions.

Here's a third test on converting improper fractions to mixed fractions.

##### Note

# What Is a Remainder?

A remainder is the amount left over after a division.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.

**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.