1.4.4

Mixed Numbers & Improper Fractions

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Mixed Numbers and Improper Fractions

Mixed numbers and improper fractions are both greater than 1.

$Improper fractions$

Improper fractions

An improper fraction has a numerator (top number) which is larger than the denominator (bottom number).
- E.g. 9 is larger than 7, so $\frac{9}{7}$ is an improper fraction.

Mixed numbers

Mixed numbers

A mixed number contains both a whole number and a normal fraction.

$Improper fraction to mixed number$

Improper fraction to mixed number

What is $\frac{26}{9}$ written as a mixed number?

$Improper fraction to mixed number$

Improper fraction to mixed number

First work out how many times the denominator (bottom number) will go into the numerator (top number).
- 9 goes into 26 two times - this is the whole number part.

$Improper fraction to mixed number$

Improper fraction to mixed number

The remainder is 26 − 18 = 8.
- So the fraction part is $\frac{8}{9}$ .

$Mixed number to improper fraction$

Mixed number to improper fraction

What is 3 $\frac{2}{5}$ written as an improper fraction?

$Mixed number to improper fraction$

Mixed number to improper fraction

Multiply the whole number by the denominator.
- Add this amount to the numerator.

$Mixed number to improper fraction$

Mixed number to improper fraction

Finish the addition.

1

Year 5 - Number

1.1

Number & Place Value

1.1.1The Value of Digits to Millions 1.1.2Smallest & Biggest Numbers to Millions 1.1.3Ordering Numbers to Millions 1.1.4Counting in Powers of 10 1.1.5Counting in Negative Numbers 1.1.6Rounding Numbers up to 1,000,000 1.1.7Reading Roman Numerals

1.2

Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers 1.2.2Written Methods for Subtracting Large Numbers 1.2.3Mental Addition & Subtraction 1.2.4Rounding to Check Your Answer

1.3

Multiplication & Division

1.3.1Multiples 1.3.2Factors 1.3.3Prime Numbers 1.3.4Prime Factors 1.3.5Composite Numbers 1.3.6Factor Trees 1.3.7Multiplication by a 1 Digit Number 1.3.8Long Multiplication Using Column Method 1.3.9Times Tables 1.3.10Division 1.3.11Multiplying & Dividing by 10, 100 & 1,000 1.3.12Square & Cube Numbers

1.4

Fractions & Decimals

1.4.1Compare & Order Fractions 1.4.2Identifying Equivalent Fractions 1.4.3Add & Subtract Fractions 1.4.4Mixed Numbers & Improper Fractions 1.4.5Multiplying Fractions by Whole Numbers 1.4.6Converting Between Decimals & Fractions 1.4.7Rounding Decimals 1.4.8Ordering Decimals

2

Year 5 - Measurement

2.1

Measures

2.1.1Metric Measurements 2.1.2Imperial Measurements

2.2

Perimeter & Area

2.2.1Perimeter 2.2.2Area

2.3

Time

2.3.1Units of Time

3

Year 5 - Geometry

3.1

Properties of 3D Shapes

3.1.1Types of 3D Shapes 3.1.2Faces, Edges & Vertices

3.2

Properties of 2D Shapes

3.3

Angles

3.3.1Angles in Degrees 3.3.2Types of Angle 3.3.3Finding Missing Angles

3.4

Position & Direction

3.4.1Reflection & Translation

4

Year 5 - Statistics

4.1

Graphs

4.1.1Line Graphs 4.1.2Tables 4.1.3Timetables

5

Year 6 - Number

5.1

Number & Place Value

5.1.1The Value of Digits to Ten Millions 5.1.2Ordering Numbers to Millions 5.1.3Rounding 5.1.4Negative Numbers

5.2

Multiplication & Division

5.2.1Multiplication by a 2 Digit Number 5.2.2Division 5.2.3Multiples 5.2.4Factors 5.2.5Primes

5.3

Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,000 5.3.2Addition & Subtraction 5.3.3Adding & Subtracting 10, 100 & 1,000 5.3.4Multiplication & Division

5.4

Order of Operations

5.5

Problem Solving

5.5.1Addition & Subtraction Multi-step Problems 5.5.2Problem Solving with Proportion

5.6

Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents 5.6.2Ordering Different Types of Fraction 5.6.3Adding & Subtracting Fractions 5.6.4Adding & Subtracting Mixed Numbers 5.6.5Multiplying Fractions 5.6.6Dividing Fractions by Whole Numbers 5.6.7Converting Between Decimals & Fractions 5.6.8Dividing Decimals

6

Year 6 - Ratio & Proportion

6.1

Ratio

6.1.1Using Ratios 6.1.2Simplifying Ratios

6.2

Percentages

6.2.1Calculating Percentages

6.3

Scale

6.3.1Scale of 2D Shapes

7

Year 6 - Algebra

7.1

Sequences

7.1.1Describing Sequences 7.1.2Finding Gaps in Sequences

7.2

Missing Number Problems

7.2.1Missing Number Problems

7.3

Equations

7.3.1Balancing Equations 7.3.2Combining Two Variables

8

Year 6 - Measurement

8.1

Problem Solving

8.1.1Problem Solving with Measures

8.2

Unit Conversion

8.2.1Conversion Between Miles & Kilometres

8.3

Perimeter, Area & Volume

8.3.1Area 8.3.2Volume 8.3.3Nets 8.3.4Faces, Edges & Vertices

8.4

Angles

8.4.1Types of Angle 8.4.2Finding Missing Angles 8.4.3Finding Missing Angles in Triangles 8.4.4Vertically Opposite Angles

8.5

Circles

8.5.1Parts of a Circle

8.6

Coordinate Grids

8.6.1Positions on Coordinate Grids 8.6.2Reflection & Translation

9

Year 6 - Statistics

9.1

Displaying Data

9.1.1Pie Charts 9.1.2Line Graphs

9.2

Averages

Jump to other topics

1

Year 5 - Number

1.1

Number & Place Value

1.1.1The Value of Digits to Millions 1.1.2Smallest & Biggest Numbers to Millions 1.1.3Ordering Numbers to Millions 1.1.4Counting in Powers of 10 1.1.5Counting in Negative Numbers 1.1.6Rounding Numbers up to 1,000,000 1.1.7Reading Roman Numerals

1.2

Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers 1.2.2Written Methods for Subtracting Large Numbers 1.2.3Mental Addition & Subtraction 1.2.4Rounding to Check Your Answer

1.3

Multiplication & Division

1.3.1Multiples 1.3.2Factors 1.3.3Prime Numbers 1.3.4Prime Factors 1.3.5Composite Numbers 1.3.6Factor Trees 1.3.7Multiplication by a 1 Digit Number 1.3.8Long Multiplication Using Column Method 1.3.9Times Tables 1.3.10Division 1.3.11Multiplying & Dividing by 10, 100 & 1,000 1.3.12Square & Cube Numbers

1.4

Fractions & Decimals

1.4.1Compare & Order Fractions 1.4.2Identifying Equivalent Fractions 1.4.3Add & Subtract Fractions 1.4.4Mixed Numbers & Improper Fractions 1.4.5Multiplying Fractions by Whole Numbers 1.4.6Converting Between Decimals & Fractions 1.4.7Rounding Decimals 1.4.8Ordering Decimals

2

Year 5 - Measurement

2.1

Measures

2.1.1Metric Measurements 2.1.2Imperial Measurements

2.2

Perimeter & Area

2.2.1Perimeter 2.2.2Area

2.3

Time

2.3.1Units of Time

3

Year 5 - Geometry

3.1

Properties of 3D Shapes

3.1.1Types of 3D Shapes 3.1.2Faces, Edges & Vertices

3.2

Properties of 2D Shapes

3.3

Angles

3.3.1Angles in Degrees 3.3.2Types of Angle 3.3.3Finding Missing Angles

3.4

Position & Direction

3.4.1Reflection & Translation

4

Year 5 - Statistics

4.1

Graphs

4.1.1Line Graphs 4.1.2Tables 4.1.3Timetables

5

Year 6 - Number

5.1

Number & Place Value

5.1.1The Value of Digits to Ten Millions 5.1.2Ordering Numbers to Millions 5.1.3Rounding 5.1.4Negative Numbers

5.2

Multiplication & Division

5.2.1Multiplication by a 2 Digit Number 5.2.2Division 5.2.3Multiples 5.2.4Factors 5.2.5Primes

5.3

Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,000 5.3.2Addition & Subtraction 5.3.3Adding & Subtracting 10, 100 & 1,000 5.3.4Multiplication & Division

5.4

Order of Operations

5.5

Problem Solving

5.5.1Addition & Subtraction Multi-step Problems 5.5.2Problem Solving with Proportion

5.6

Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents 5.6.2Ordering Different Types of Fraction 5.6.3Adding & Subtracting Fractions 5.6.4Adding & Subtracting Mixed Numbers 5.6.5Multiplying Fractions 5.6.6Dividing Fractions by Whole Numbers 5.6.7Converting Between Decimals & Fractions 5.6.8Dividing Decimals

6

Year 6 - Ratio & Proportion

6.1

Ratio

6.1.1Using Ratios 6.1.2Simplifying Ratios

6.2

Percentages

6.2.1Calculating Percentages

6.3

Scale

6.3.1Scale of 2D Shapes

7

Year 6 - Algebra

7.1

Sequences

7.1.1Describing Sequences 7.1.2Finding Gaps in Sequences

7.2

Missing Number Problems

7.2.1Missing Number Problems

7.3

Equations

7.3.1Balancing Equations 7.3.2Combining Two Variables

8

Year 6 - Measurement

8.1

Problem Solving

8.1.1Problem Solving with Measures

8.2

Unit Conversion

8.2.1Conversion Between Miles & Kilometres

8.3

Perimeter, Area & Volume

8.3.1Area 8.3.2Volume 8.3.3Nets 8.3.4Faces, Edges & Vertices

8.4

Angles

8.4.1Types of Angle 8.4.2Finding Missing Angles 8.4.3Finding Missing Angles in Triangles 8.4.4Vertically Opposite Angles

8.5

Circles

8.5.1Parts of a Circle

8.6

Coordinate Grids

8.6.1Positions on Coordinate Grids 8.6.2Reflection & Translation

9

Year 6 - Statistics

9.1

Displaying Data

9.1.1Pie Charts 9.1.2Line Graphs

9.2

Averages

Practice questions on Mixed Numbers & Improper Fractions

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

1
What is 2$$\frac{3}{4}$$ written as an improper fraction?Multiple choice
2
What is 5$$\frac{1}{5}$$ written as an improper fraction?Multiple choice
3
What is $$\frac{31}{8}$$ written as a mixed number?Multiple choice
4
What is $$\frac{25}{4}$$ written as a mixed number?Multiple choice
5
Which of the following conversions are correct?True / false

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Add & Subtract Fractions

Multiplying Fractions by Whole Numbers