Source: https://senecalearning.com/en-gb/revision-notes/11/maths/11-maths/2-2-2-converting-mixed-numbers-to-improper-fractions

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# Converting Mixed Numbers to Improper Fractions

11+ Maths, topic 2.2.2

## Converting Mixed Numbers to Improper Fractions

You can convert mixed numbers to improper fractions. Look at this example, using the mixed number 12⁄3.

### Step 1

![Step 1](https://image-v2.cdn.app.senecalearning.com/2019-05/79566d4e-a4cc-4896-825a-9fb43bd7e536/Mixed-Number-To-Improper-Fraction-Concept1.png)

- Look at the denominator (the bottom number). This number will stay the same.
 - So the mixed number will have a denominator of 3.

### Step 2

![Step 2](https://image-v2.cdn.app.senecalearning.com/2019-05/deac46fe-c786-4a6a-865f-26fa526a31b6/Mixed-Number-To-Improper-Fraction-Concept2.png)

- Look at the whole number. Multiply this number by the denominator. 
 - 1 × 3 = 3

### Step 3

![Step 3](https://image-v2.cdn.app.senecalearning.com/2019-05/249b269b-96cd-4276-8124-c620c4260a94/Mixed-Number-To-Improper-Fraction-Concept3%20(2).png)

- Add the number from step 2 to the numerator (the top number).
 - 2 + 3 = 5
   - This number will be the numerator in the improper fraction.

### The answer

![The answer](https://image-v2.cdn.app.senecalearning.com/2019-05/31db8295-0d5e-47bf-9c7f-9d7a9400c0bf/Mixed-Number-To-Improper-Fraction-Concept3.png)

- The mixed number 12⁄3 is 5⁄3 as an improper fraction.

## Test yourself on Converting Mixed Numbers to Improper Fractions

- What is 33⁄5 as an improper fraction?
- What is 42⁄9 as an improper fraction?
- What is 51⁄6 as an improper fraction?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/f4a9de91-3dcc-4e19-b180-1286357dded5/section/48cbdb79-214d-4e5c-b3aa-48e9b43f8839/session)

- Previous topic: [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)
- Next topic: [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)

## 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)