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Problem solving with fractions and decimals

I can use my knowledge of fractions and decimals to solve problems.

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Lesson 18 of 18

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Year 7

Problem solving with fractions and decimals

I can use my knowledge of fractions and decimals to solve problems.

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Lesson details

Key learning points

Fractions can be used to solve problems in context.
Converting to decimals may be useful to solve problems in context.
It may be necessary to order a set of fractions and decimals to solve problems in context.
Fractions and decimals can be useful in solving in many real world problems.

Keywords

Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Proportion - Proportion is a part to whole (sometimes part to part) comparison.

Common misconception

Assuming that there are 100 minutes in an hour and converting 3.25 hours to 3 hours 25 minutes.

Start with half an hour, pupils should be happy that half an hour is 30 mins, show it written as a decimal to highlight it's not 3.3 hours

At the beginning of the lesson have this question write on the board for pupils to consider as they enter the room. 'An ant starts 1 m away from a wall, each minute it moves half the distance to the wall. Will it ever reach the wall?'

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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.
Two fractions are if they have the same value.

Correct Answer: equivalent

Q2.
Andeep writes down the number 0.99 Select all the numbers below that are greater than Andeep's number.

0.98

0.99

0.909

Correct answer: 0.991

Q3.
I am rolling a six sided dice and filling in two grids. Select the numbers that can replace $$a$$ so that the number in the first grid will be less than the number in the second grid.

Correct answer: 2

Correct answer: 3

Correct answer: 4

Q4.
I am rolling a six sided dice and filling in two grids. If $$a$$ = 5, which of the following numbers can replace $$b$$ so that the second number is less?

Correct answer: 2

Correct answer: 3

Correct answer: 4

Q5.
What fraction is halfway between $$\frac{8}{11}$$ and $$\frac{10}{11}$$?

$$\frac{9}{22}$$

Correct answer: $$\frac{99}{121}$$

Correct answer: $$\frac{153}{187}$$

$$\frac{104}{143}$$

Q6.
What fraction is halfway between $$\frac{4}{7}$$ and $$1$$?

$$\frac{8}{14}$$

$$\frac{9}{14}$$

$$\frac{10}{14}$$

Correct answer: $$\frac{11}{14}$$

$$\frac{12}{14}$$

Assessment exit quiz

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6 Questions

Q1.
is a part to whole (sometimes part to part) comparison.

Correct Answer: Proportion, proportion

Q2.
To compare $$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$$ and $$\frac{5}{6}$$ which common denominator would be the most efficient?

$$6$$

$$8$$

Correct answer: $$12$$

$$24$$

Q3.
Izzy, Andeep, Lucas, Alex and Sam took part in a quiz. Below are the proportions for how many questions they each got right. Order them from worst to best.

1 - Alex $$\frac{17}{30}$$

2 - Lucas $$\frac{3}{5}$$

3 - Izzy $$\frac{2}{3}$$

4 - Andeep $$\frac{11}{15}$$

5 - Sam $$\frac{9}{10}$$

Q4.
Jacob buys a drink and an ice cream. He also wants to buy a cupcake. He has £5. Can he afford to buy the cupcake?

Yes - he has £2.51 left to spend which is more than enough

Yes - he has exactly £1.58 left to spend which is the cost of the cupcake

No - he has spent £4.49

Correct answer: No - he has £1.51 left to spend which is not enough

Q5.
Which item is the third most expensive?

cupcake

apple

ice cream

banana

Correct answer: drink

Q6.
A rectangle has a length of $$0.82$$ m and a width of $$\frac{2}{5}$$ m. What is the perimeter of the rectangle? Give your answer in decimal form.

Correct Answer: 2.44 m, 2.44m, 244cm, 244 cm

Lesson appears in

UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

Maths

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Problem solving with fractions and decimals

Problem solving with fractions and decimals

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Two fractions are if they have the same value.

Q2.Andeep writes down the number 0.99 Select all the numbers below that are greater than Andeep's number.

Q3.I am rolling a six sided dice and filling in two grids. Select the numbers that can replace $$a$$ so that the number in the first grid will be less than the number in the second grid.

Q4.I am rolling a six sided dice and filling in two grids. If $$a$$ = 5, which of the following numbers can replace $$b$$ so that the second number is less?

Q5.What fraction is halfway between $$\frac{8}{11}$$ and $$\frac{10}{11}$$?

Q6.What fraction is halfway between $$\frac{4}{7}$$ and $$1$$?

Assessment exit quiz

6 Questions

Q1. is a part to whole (sometimes part to part) comparison.

Q2.To compare $$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$$ and $$\frac{5}{6}$$ which common denominator would be the most efficient?

Q3.Izzy, Andeep, Lucas, Alex and Sam took part in a quiz. Below are the proportions for how many questions they each got right. Order them from worst to best.

Q4.Jacob buys a drink and an ice cream. He also wants to buy a cupcake. He has £5. Can he afford to buy the cupcake?

Q5.Which item is the third most expensive?

Q6.A rectangle has a length of $$0.82$$ m and a width of $$\frac{2}{5}$$ m. What is the perimeter of the rectangle? Give your answer in decimal form.

Lesson appears in

UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

Maths

Q1.
Two fractions are if they have the same value.

Q2.
Andeep writes down the number 0.99 Select all the numbers below that are greater than Andeep's number.

Q3.
I am rolling a six sided dice and filling in two grids. Select the numbers that can replace $$a$$ so that the number in the first grid will be less than the number in the second grid.

Q4.
I am rolling a six sided dice and filling in two grids. If $$a$$ = 5, which of the following numbers can replace $$b$$ so that the second number is less?

Q5.
What fraction is halfway between $$\frac{8}{11}$$ and $$\frac{10}{11}$$?

Q6.
What fraction is halfway between $$\frac{4}{7}$$ and $$1$$?

Q1.
is a part to whole (sometimes part to part) comparison.

Q2.
To compare $$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$$ and $$\frac{5}{6}$$ which common denominator would be the most efficient?

Q3.
Izzy, Andeep, Lucas, Alex and Sam took part in a quiz. Below are the proportions for how many questions they each got right. Order them from worst to best.

Q4.
Jacob buys a drink and an ice cream. He also wants to buy a cupcake. He has £5. Can he afford to buy the cupcake?

Q5.
Which item is the third most expensive?

Q6.
A rectangle has a length of $$0.82$$ m and a width of $$\frac{2}{5}$$ m. What is the perimeter of the rectangle? Give your answer in decimal form.