Compose and decompose mixed numbers

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Lesson details

Learning outcome

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

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.

Teacher tip

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.

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).

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Prior knowledge starter quiz

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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

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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

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Compose and decompose mixed numbers

Lesson slides

Lesson details

Learning outcome

Key learning points

Keywords

Common misconception

Teacher tip

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?

How to plan a lesson using our resources

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?