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Solve problems involving mixed numbers

I can solve problems involving mixed numbers.

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Year 4

Solve problems involving mixed numbers

I can solve problems involving mixed numbers.

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Lesson details

Key learning points

Word problems can involve mixed numbers. Mixed numbers may be used as part of the question or may form the answer.
Mixed numbers can be used to represent measures.
Representing problems as part-part-whole model can support us to form equations that we can then solve.

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 solving word problems, stick with standard partitioning of mixed numbers to really embed this concept. Measures often use halves, quarters, fifths and tenths as the most common unit for the fractional part.

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).

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Prior knowledge starter quiz

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6 Questions

Q1.
Look at this mixed number $$2{{3} \over {9}}$$ We say it as and three one-ninths.

Correct Answer: two, 2

Q2.
Look at this mixed number $$5{{1} \over {6}}$$ We say it as ‘five and one- .

Correct Answer: sixth

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

Correct Answer: 250

Q4.
Look at the part-part-whole model. $$6{{2} \over {3}}$$ is composed of 6 and two- .

Correct Answer: thirds

Q5.
Select the correct sum. 7 + $$ {2} \over {5}$$ = ?

$$2{{7} \over {5}}$$

$$2{{5} \over {7}}$$

$$7{{5} \over {2}}$$

Correct answer: $$7{{2} \over {5}}$$

$$5{{2} \over {7}}$$

Q6.
$$18{{3} \over {9}}$$ − $$ {3} \over {9}$$ = ?

Correct answer: 18

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

Assessment exit quiz

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6 Questions

Q1.
Which model below represents this problem? Jacob listens to music for two hours on Monday and for half an hour on Tuesday. How long does he listen to music for in total?

Correct Answer: An image in a quiz

Q2.
Which model below represents this situation? Jacob bakes a cake. The mass of the cake is one and a quarter kg. He gives some cake to his friends then measures the mass left to be one kg.

Correct answer: B

Q3.
Look at the part-part-whole model, which equations can be formed from it?

6 - $$ {1} \over {4}$$ = ?

Correct answer: 6 + $$ {1} \over {4}$$ = ?

Correct answer: $$ {1} \over {4}$$ + 6 = ?

$$ {1} \over {4}$$ - 6 = ?

Q4.
Look at the part-part-whole model, which equations can be formed from it?

? = 11 + $$11{{1} \over {8}}$$

11 + $$11{{1} \over {8}}$$ = ?

$$11{{1} \over {8}}$$ + 11 = ?

Correct answer: $$11{{1} \over {8}}$$ - ? = 11

Correct answer: $$11{{1} \over {8}}$$ - 11 = ?

Q5.
Jacob has two and five-tenths of a metre length of ribbon. He uses two metres of it. How much ribbon does he have left over?

One metre

Two metres

Correct answer: $$ {5} \over {10}$$ of a metre

$$ {10} \over {5}$$ of a metre

Ten metres

Q6.
Sofia has a kitten that has a mass of one kilogram. When she next measures its mass, it is eight-tenths of a kilogram heavier. What is its mass now in kilograms?

8 kg

10 kg

Correct answer: $$1{{8} \over {10}}$$ kg

$$1{{10} \over {8}}$$ kg

$$8{{1} \over {10}}$$ kg

Lesson appears in

UnitMaths / Composition of fractions greater than one

Maths

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Solve problems involving mixed numbers

Solve problems involving 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 $$2{{3} \over {9}}$$ We say it as and three one-ninths.

Q2.Look at this mixed number $$5{{1} \over {6}}$$ We say it as ‘five and one- .

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

Q4.Look at the part-part-whole model. $$6{{2} \over {3}}$$ is composed of 6 and two- .

Q5.Select the correct sum. 7 + $$ {2} \over {5}$$ = ?

Q6.$$18{{3} \over {9}}$$ − $$ {3} \over {9}$$ = ?

Assessment exit quiz

6 Questions

Q1.Which model below represents this problem? Jacob listens to music for two hours on Monday and for half an hour on Tuesday. How long does he listen to music for in total?

Q2.Which model below represents this situation? Jacob bakes a cake. The mass of the cake is one and a quarter kg. He gives some cake to his friends then measures the mass left to be one kg.

Q3.Look at the part-part-whole model, which equations can be formed from it?

Q4.Look at the part-part-whole model, which equations can be formed from it?

Q5.Jacob has two and five-tenths of a metre length of ribbon. He uses two metres of it. How much ribbon does he have left over?

Q6.Sofia has a kitten that has a mass of one kilogram. When she next measures its mass, it is eight-tenths of a kilogram heavier. What is its mass now in kilograms?

Lesson appears in

UnitMaths / Composition of fractions greater than one

Maths

Q1.
Look at this mixed number $$2{{3} \over {9}}$$ We say it as and three one-ninths.

Q2.
Look at this mixed number $$5{{1} \over {6}}$$ We say it as ‘five and one- .

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

Q4.
Look at the part-part-whole model. $$6{{2} \over {3}}$$ is composed of 6 and two- .

Q5.
Select the correct sum. 7 + $$ {2} \over {5}$$ = ?

Q6.
$$18{{3} \over {9}}$$ − $$ {3} \over {9}$$ = ?

Q1.
Which model below represents this problem? Jacob listens to music for two hours on Monday and for half an hour on Tuesday. How long does he listen to music for in total?

Q2.
Which model below represents this situation? Jacob bakes a cake. The mass of the cake is one and a quarter kg. He gives some cake to his friends then measures the mass left to be one kg.

Q3.
Look at the part-part-whole model, which equations can be formed from it?

Q4.
Look at the part-part-whole model, which equations can be formed from it?

Q5.
Jacob has two and five-tenths of a metre length of ribbon. He uses two metres of it. How much ribbon does he have left over?

Q6.
Sofia has a kitten that has a mass of one kilogram. When she next measures its mass, it is eight-tenths of a kilogram heavier. What is its mass now in kilograms?