Source: https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-1-simplifying-fractions

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# Simplifying Fractions

11+ Maths, topic 2.1.1

## Simplifying Fractions

You need to know how to 'cancel down' fractions to their simplest forms.

### Example - simplify 20⁄24

![Example - simplify 20⁄24](https://image-v2.cdn.app.senecalearning.com/2019-06/86fb5655-9112-495d-a72c-e4d19d3c7f27/SimplifyingFractions-Concept%20(1).png)

### How to simplify the fraction

![How to simplify the fraction](https://image-v2.cdn.app.senecalearning.com/2019-06/4b1dbe3c-2e13-46b6-ba30-47030d0494c3/SimplifyingFractions-Concept%20(2).png)

- To simplify the fraction 20⁄24, we need to find the largest number that we can divide both 20 and 24 by.

### Numbers that 20 can be divided by

![Numbers that 20 can be divided by](https://image-v2.cdn.app.senecalearning.com/2019-06/68c08675-1f91-4241-9324-bcc57185bf01/Copy%20of%20SimplifyingFractions-Concept%20(2).png)

- The factors of 20 are 1, 2, 4, 5, 10 and 20.

### Numbers that 24 can be divided by

![Numbers that 24 can be divided by](https://image-v2.cdn.app.senecalearning.com/2019-06/0aec528a-b7fd-4cd6-8989-eecdf31fe70f/Copy%20of%20Copy%20of%20SimplifyingFractions-Concept%20(1).png)

- The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

### Find the largest shared number

![Find the largest shared number](https://image-v2.cdn.app.senecalearning.com/2019-06/82b94752-edeb-4280-9d0a-d612b98e64fb/SimplifyingFractions-Concept-Answer.png)

- The largest common factor is 4. 
- So we need to divide both 20 and 24 by 4 to simplify the fraction.

### Divide 20 and 24 by 4

![Divide 20 and 24 by 4](https://image-v2.cdn.app.senecalearning.com/2019-06/1b4216be-6503-4f12-abbd-ed0acec154fe/SimplifyingFractions-Concept-Divideby4.png)

- The simplest form of the fraction 20⁄24 is 5⁄6

## Test yourself on Simplifying Fractions

- Which number do you need to divide the top and bottom numbers by to write the fraction 11⁄22 in its simplest form?
- Which fractions are in their simplest forms?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/f4a9de91-3dcc-4e19-b180-1286357dded5/section/aff54abe-502b-4426-badf-6481f77dee70/session)

- Previous topic: [1.5.1 Angles in a Triangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-5-1-angles-in-a-triangle.md)
- Next topic: [2.1.2 Identifying Equivalent Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-2-identifying-equivalent-fractions.md)

## 11+ Maths contents

### 1 Angles
- 1.1 7 Facts About Angles
  - [1.1.1 Facts About Angles](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-1-1-facts-about-angles.md)
  - [1.1.2 More Facts About Angles](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-1-2-more-facts-about-angles.md)
- 1.2 Identify the Angle
  - [1.2.1 Identify the Angle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-2-1-identify-the-angle.md)
- 1.3 Angles on a Straight Line
  - [1.3.1 Angles on a Straight Line](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-3-1-angles-on-a-straight-line.md)
  - [1.3.2 Angles on a Straight Line - Practice Questions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-3-2-angles-on-a-straight-line-practice-questions.md)
- 1.4 Angles in a Circle
  - [1.4.1 Angles in a Circle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-4-1-angles-in-a-circle.md)
- 1.5 Angles in Triangles
  - [1.5.1 Angles in a Triangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/1-5-1-angles-in-a-triangle.md)

### 2 Fractions
- 2.1 Simplifying Fractions
  - [2.1.1 Simplifying Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-1-simplifying-fractions.md)
  - [2.1.2 Identifying Equivalent Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-1-2-identifying-equivalent-fractions.md)
- 2.2 Improper Fractions & Mixed Numbers
  - [2.2.1 Improper Fractions & Mixed Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-1-improper-fractions-and-mixed-numbers.md)
  - [2.2.2 Converting Mixed Numbers to Improper Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-2-converting-mixed-numbers-to-improper-fractions.md)
  - [2.2.3 Converting Improper Fractions to Mixed Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-3-converting-improper-fractions-to-mixed-numbers.md)
- 2.3 Fractions of Numbers
  - [2.3.1 Fractions of Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-3-1-fractions-of-numbers.md)
- 2.4 Expressing Shaded Areas as Fractions
  - [2.4.1 Expressing Shaded Areas as Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-4-1-expressing-shaded-areas-as-fractions.md)

### 3 Time
- 3.1 12-Hour & 24-Hour Clocks
  - [3.1.1 Difference Between 12-Hour & 24-Hour Clocks](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-1-difference-between-12-hour-and-24-hour-clocks.md)
  - [3.1.2 Changing the 12-Hour Clock to the 24-Hour Clock](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-2-changing-the-12-hour-clock-to-the-24-hour-clock.md)
  - [3.1.3 Changing the 24-hour Clock to the 12-Hour Clock](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-1-3-changing-the-24-hour-clock-to-the-12-hour-clock.md)
- 3.2 Time-Related Problems
  - [3.2.1 Time-Related Problems](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-2-1-time-related-problems.md)
  - [3.2.2 Timetable & Schedule Problems](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/3-2-2-timetable-and-schedule-problems.md)

### 4 Prime Numbers
- 4.1 Prime Numbers
  - [4.1.1 Prime Numbers](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/4-1-1-prime-numbers.md)

### 5 Probability
- 5.1 Probability
  - [5.1.1 Probability Scale](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-1-probability-scale.md)
  - [5.1.2 Probability Fractions](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-2-probability-fractions.md)
  - [5.1.3 Experimental Probability](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/5-1-3-experimental-probability.md)

### 6 Ratio
- 6.1 Ratios
  - [6.1.1 Ratios](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/6-1-1-ratios.md)

### 7 Sequences
- 7.1 Constant Sequences
  - [7.1.1 Constant Increase Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-1-1-constant-increase-sequences.md)
  - [7.1.2 Constant Decrease Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-1-2-constant-decrease-sequences.md)
- 7.2 Doubling & Halving Sequences
  - [7.2.1 Doubling Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-2-1-doubling-sequences.md)
  - [7.2.2 Halving Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-2-2-halving-sequences.md)
- 7.3 Alternating Patterns & Two-Step Sequences
  - [7.3.1 Alternating Pattern Sequences](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-3-1-alternating-pattern-sequences.md)
- 7.4 Two-Step Patterns
  - [7.4.1 Two-Step Patterns](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-4-1-two-step-patterns.md)
- 7.5 The nth Term
  - [7.5.1 Find the nth Term](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-1-find-the-nth-term.md)
  - [7.5.2 Using the nth Term](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/7-5-2-using-the-nth-term.md)

### 8 Area & Perimeter
- 8.1 Perimeter of a Quadrilateral
  - [8.1.1 Finding the Perimeter of a Quadrilateral](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-1-1-finding-the-perimeter-of-a-quadrilateral.md)
  - [8.1.2 Finding the Missing Length](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-1-2-finding-the-missing-length.md)
- 8.2 Area of a Quadrilateral
  - [8.2.1 Finding the Area of a Quadrilateral](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-1-finding-the-area-of-a-quadrilateral.md)
  - [8.2.2 Finding the Missing Side of a Rectangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-2-finding-the-missing-side-of-a-rectangle.md)
  - [8.2.3 Finding the Missing Side of a Square](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-3-finding-the-missing-side-of-a-square.md)
  - [8.2.4 Finding the Area of Irregular Shapes](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-2-4-finding-the-area-of-irregular-shapes.md)
- 8.3 Area of a Triangle
  - [8.3.1 Finding the Area of a Triangle](https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/8-3-1-finding-the-area-of-a-triangle.md)