New

Compose and decompose mixed numbers

I can compose and decompose mixed numbers to solve addition and subtraction calculations.

Download all

View unit

Lesson 3 of 5

New

Year 4

Compose and decompose mixed numbers

I can compose and decompose mixed numbers to solve addition and subtraction calculations.

Download all

Lesson slides

Download lesson slides

Skip lesson slides

Lesson details

Key learning points

Mixed numbers are quantities that are made up of a whole number part and a fractional part.
Addition and subtraction calculations represent how mixed numbers can be composed or decomposed.
Knowing how mixed numbers are composed, supports us to solve addition and subtraction calculations.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined into one "mixed" number. For example: one and a half is a mixed number.

Common misconception

Children may be confused about how to write mixed numbers. Children may say 'five and one-eight, rather than five and one-eighth.

As a school, establish how mixed numbers will be recorded so that you have consistency. Ensure children are accurately expressing the fraction part.

When calculating, stick with standard partitioning of mixed numbers to really embed this concept. Present addition equations with the whole number as the first addend and then with the fractional part as the first addend.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Prior knowledge starter quiz

Download quiz pdf

6 Questions

Q1.
Look at this mixed number $$7{{2} \over {10}}$$ We say it as and two one-tenths.

Correct Answer: seven, 7

Q2.
Look at this mixed number $$3{{4} \over {5}}$$ We say it as ‘three and four- .

Correct Answer: fifths

Q3.
Look at the part-part-whole model. What is the missing part?

Correct Answer: 200

Q4.
Jacob runs 160 metres and Sofia runs 140 metres. What is the total distance that they have run? m

Correct Answer: 300

Q5.
Look at the part-part-whole model. $$8{{2} \over {10}}$$ is composed of 8 and two- .

Correct Answer: tenths

Q6.
Which addition expression represents the composition of the mixed number, $$3{{2} \over {6}}$$?

2 + $$ {3} \over {6}$$

2 + $$ {6} \over {3}$$

Correct answer: 3 + $$ {2} \over {6}$$

3 + $$ {6} \over {2}$$

6 + $$ {2} \over {3}$$

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Select the correct sum. 8 + $$ {3} \over {12}$$ = ?

$$3{{8} \over {12}}$$

$$3{{12} \over {8}}$$

$$8{{12} \over {3}}$$

Correct answer: $$8{{3} \over {12}}$$

$$1{{3} \over {8}}$$

Q2.
$$5{{4} \over {6}}$$ − 5 = ?

$$ {5} \over {6}$$

Correct answer: $$ {4} \over {6}$$

$$ {6} \over {4}$$

$$ {6} \over {5}$$

Q3.
5 + $$ {4} \over {9}$$ + 12 = ?

$$5{{4} \over {17}}$$

$$12{{5} \over {9}}$$

Correct answer: $$17{{4} \over {9}}$$

$$17{{9} \over {4}}$$

Q4.
$$12{{3} \over {4}}$$ − $$ {3} \over {4}$$ = ?

Correct answer: 12

$$ {3} \over {4}$$

Q5.
Jacob has been given a three and a two-tenths metres length of wool. He cuts a piece of wool that is three metres and gives it to Sofia. How much wool does he have left?

2 metres

3 metres

10 metres

Correct answer: $$ {2} \over {10}$$ metre

$$ {10} \over {2}$$ metre

Q6.
Sofia has been given a container with nine and three-quarters of water in it. After she has spilt it, there is three-quarters of a litre of water left. How much did she spill?

$$ {3} \over {9}$$ litres

$$ {3} \over {4}$$ litres

3 litres

Correct answer: 9 litres

Lesson appears in

UnitMaths / Composition of fractions greater than one

Maths

Show unit

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Compose and decompose mixed numbers

Compose and decompose mixed numbers

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Look at this mixed number $$7{{2} \over {10}}$$ We say it as and two one-tenths.

Q2.Look at this mixed number $$3{{4} \over {5}}$$ We say it as ‘three and four- .

Q3.Look at the part-part-whole model. What is the missing part?

Q4.Jacob runs 160 metres and Sofia runs 140 metres. What is the total distance that they have run? m

Q5.Look at the part-part-whole model. $$8{{2} \over {10}}$$ is composed of 8 and two- .

Q6.Which addition expression represents the composition of the mixed number, $$3{{2} \over {6}}$$?

Assessment exit quiz

6 Questions

Q1.Select the correct sum. 8 + $$ {3} \over {12}$$ = ?

Q2.$$5{{4} \over {6}}$$ − 5 = ?

Q3.5 + $$ {4} \over {9}$$ + 12 = ?

Q4.$$12{{3} \over {4}}$$ − $$ {3} \over {4}$$ = ?

Q5.Jacob has been given a three and a two-tenths metres length of wool. He cuts a piece of wool that is three metres and gives it to Sofia. How much wool does he have left?

Q6.Sofia has been given a container with nine and three-quarters of water in it. After she has spilt it, there is three-quarters of a litre of water left. How much did she spill?

Lesson appears in

UnitMaths / Composition of fractions greater than one

Maths

Q1.
Look at this mixed number $$7{{2} \over {10}}$$ We say it as and two one-tenths.

Q2.
Look at this mixed number $$3{{4} \over {5}}$$ We say it as ‘three and four- .

Q3.
Look at the part-part-whole model. What is the missing part?

Q4.
Jacob runs 160 metres and Sofia runs 140 metres. What is the total distance that they have run? m

Q5.
Look at the part-part-whole model. $$8{{2} \over {10}}$$ is composed of 8 and two- .

Q6.
Which addition expression represents the composition of the mixed number, $$3{{2} \over {6}}$$?

Q1.
Select the correct sum. 8 + $$ {3} \over {12}$$ = ?

Q2.
$$5{{4} \over {6}}$$ − 5 = ?

Q3.
5 + $$ {4} \over {9}$$ + 12 = ?

Q4.
$$12{{3} \over {4}}$$ − $$ {3} \over {4}$$ = ?

Q5.
Jacob has been given a three and a two-tenths metres length of wool. He cuts a piece of wool that is three metres and gives it to Sofia. How much wool does he have left?

Q6.
Sofia has been given a container with nine and three-quarters of water in it. After she has spilt it, there is three-quarters of a litre of water left. How much did she spill?