- 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

## Question

Convert the improper fraction below to a mixed fraction.## Step-by-Step:

## 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

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

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

## Answer:

2^{1}/

_{2}(two and a half) is

^{5}/

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

## 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

## 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.- 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.

## You might also like...

fractionsunderstanding mixed fractionsconverting improper to mixed fractionsunderstanding equivalent fractions and simplest form

#### Help Us Improve Mathematics Monster

- Do you disagree with something on this page?
- Did you spot a typo?

__this form__.

#### Find Us Quicker!

- When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add
**#mm**to your search term.

#### Share This Page

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, __please tell us__. It helps us a lot!

#### Create a QR Code

Use our handy widget to create a QR code for this page...or any page.