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Lesson 5 of 5

Solve problems involving addition and subtraction of mixed numbers

I can solve problems involving the addition and subtraction of mixed numbers.

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Lesson 5 of 5
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Solve problems involving addition and subtraction of mixed numbers

I can solve problems involving the addition and subtraction of mixed numbers.

Lesson details

Key learning points

  1. Improper fractions can be added and subtracted in the same way as proper fractions.
  2. When interpreting data or solving problems, number-sense is needed to determine the most efficient strategy to use.
  3. Decide on the most efficient strategy by looking at the fractions of the minuend and subtrahend.
  4. Bar models are a useful tool to represent word problems and support in forming an equation to solve.

Keywords

  • Mixed number - A mixed number is a whole number and a fraction combined.

  • Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Common misconception

Children may not always choose an efficient strategy when adding or subtracting mixed numbers. This may result in calculation errors being made.

Look at the numbers in the calculation. What do you notice? Which strategy would be most efficient to use with these numbers? Check your answer using a different strategy. If you get the same answer, you are likely to be correct.

Children need to have a secure understanding of how to add and subtract proper fractions and mixed numbers and how to convert between mixed numbers and improper fractions.
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

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Prior knowledge starter quiz

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6 Questions

Q1.
Look at this calculation: $$ {4} \over {10}$$ − $$ {3} \over {10}$$ What is the unit we are working with?

thirds
quarters
fifths
Correct answer: tenths

Q2.
$$2{{4} \over {5}}$$ + $$1{{3} \over {5}}$$ =

$$ {37} \over {5}$$
$$3{7} \over {10}$$
Correct answer: $$4{{2} \over {5}}$$
$$4{{2} \over {10}}$$
$$1{{1} \over {5}}$$

Q3.
$$3{{4} \over {5}}$$ − $$1{{3} \over {5}}$$ =

$$4{{7} \over {5}}$$
$$4{{7} \over {10}}$$
$$ {1} \over {5}$$
$$ {1} \over {0}$$
Correct answer: $$2{{1} \over {5}}$$

Q4.
Use ‘finding the difference’ by counting on to solve $$8{{2} \over {9}}$$ − $$7{{8} \over {9}}$$

$$15{{10} \over {9}}$$
$$15{{10} \over {18}}$$
$$1{{6} \over {9}}$$
Correct answer: $$ {3} \over {9}$$
$$1{{3} \over {9}}$$

Q5.
Match the mixed number to their equivalent improper fraction.

Correct Answer:$$1{{4} \over {5}}$$,$$ {9} \over {5}$$

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

Correct Answer:$$4{{4} \over {5}}$$,$$ {24} \over {5}$$

$$ {24} \over {5}$$

Correct Answer:$$2{{4} \over {5}}$$,$$ {14} \over {5}$$

$$ {14} \over {5}$$

Correct Answer:$$5{{1} \over {5}}$$,$$ {26} \over {5}$$

$$ {26} \over {5}$$

Correct Answer:$$3{{3} \over {5}}$$ ,$$ {18} \over {5}$$

$$ {18} \over {5}$$

Q6.
By expressing the mixed numbers as improper fractions, calculate this: $$7{{3} \over {8}}$$ − $$2{{5} \over {8}}$$ =

Correct answer: $$4{{6} \over {8}}$$
$$9{{8} \over {8}}$$
10
$$5{{2} \over {8}}$$
6

Assessment exit quiz

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6 Questions

Q1.
Which bar model represents this problem? Izzy eats one and one-quarter slices of pizza. How much less pizza does she eat than Andeep who has eaten two and three-quarter slices of pizza?

An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

Q2.
Look at the table. How far does Izzy walk over Monday and Tuesday in all?

An image in a quiz
$$ {45} \over {5}$$
Correct answer: 5
$$5{{3} \over {5}}$$
$$3{{4} \over {5}}$$

Q3.
Look at the table. How far does Izzy walk over Tuesday and Wednesday in total?

An image in a quiz
$$ {56} \over {5}$$
6
Correct answer: $$6{{1} \over {5}}$$
$$5{{1} \over {5}}$$

Q4.
Look at the table. How much further does Izzy walk on Wednesday than Thursday?

An image in a quiz
$$4{{5} \over {5}}$$
5
$$2{{1} \over {5}}$$
Correct answer: $$1{{4} \over {5}}$$

Q5.
Andeep has a five and five-tenths metres of rope. He cuts a piece off. He has three and two-tenth metres left. What length of rope did he cut off?

$$2{{7} \over {10}}$$
Correct answer: $$2{{3} \over {10}}$$
$$8{{7} \over {10}}$$
$$2{{3} \over {0}}$$
$$1{{3} \over {10}}$$

Q6.
Izzy spends two and three-quarter hours in the park on Saturday and another two and two-quarter hours on Sunday. How long does she spend in the park in total?

$$4{{5} \over {8}}$$
$$2{{5} \over {8}}$$
Correct answer: $$5{{1} \over {4}}$$
$$ {1} \over {4}$$
$$4{{6} \over {4}}$$

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UnitMaths / Efficient strategies for adding and subtracting mixed numbers (crossing a whole)

Maths

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