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# Converting mixed numbers to improper fractions
- URL: https://www.esheets.io/converting-mixed-numbers-to-improper-fractions/
- Published: 2025-01-08T19:04:31.000Z
- Updated: 2026-06-21T17:54:18.000Z
- Author: Richard Linnington
- Tags: Maths, Number

Converting mixed numbers to improper fractions is a key skill in mathematics, often used in real-world situations like doubling recipes or measuring materials for construction. It helps you work more easily with fractions when performing calculations like addition, subtraction, or multiplication. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise converting mixed numbers to improper fractions with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Multiplying the whole number by the denominator.
- Adding the numerator.
- Keeping the same denominator.
- Writing the result as an improper fraction.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Convert these mixed numbers to improper fractions.

## Topic guide

### What this worksheet practises

This worksheet provides practice on converting mixed numbers (a whole number and a fraction) into improper fractions (where the top number is bigger than the bottom). This is a crucial first step before multiplying or dividing fractions, as those operations cannot be easily done with mixed numbers.

### Key method

To convert a mixed number to an improper fraction, you need to turn the whole number parts into fraction parts of the same size, and add them to the existing fraction.

- Identify the whole number, the numerator (top), and the denominator (bottom).
- Multiply the whole number by the denominator. This tells you how many pieces the whole numbers are made of.
- Add the numerator to this result. This gives you the total number of pieces.
- Write this new total over the original denominator.

### Worked example

**Convert 3⅖ into an improper fraction.**

Step 1: Identify the parts. Whole number = 3, numerator = 2, denominator = 5.

Step 2: Multiply the whole number by the denominator.

3 × 5 = 15.

Step 3: Add the existing numerator.

15 + 2 = 17.

Step 4: Put this over the original denominator.

The answer is 17/5.

### Common mistakes to avoid

The most common error is adding instead of multiplying in the first step. For example, calculating 3 + 5 instead of 3 × 5\. Always remember: the whole number tells you how many "lots" of the denominator you have.

### How to check your answer

To check your work, perform the reverse operation. Divide your new numerator by the denominator. 17 ÷ 5 goes 3 times, with a remainder of 2\. So, it is 3 whole ones and 2 leftover fifths (3⅖). This proves your calculation is exactly right.