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Lesson 12 of 17
New
New
- Year 7
Dividing a quantity into a given ratio
I can divide one quantity into a given ratio.
Lesson details
Key learning points
- Context can make it easier to divide a quantity into a given ratio.
- Bar models can help to represent a situation.
- It is important that the parts are equal, otherwise the ratio is not represented correctly.
Keywords
Proportion - Variables are in proportion if they have a constant multiplicative relationship.
Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Common misconception
Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'.
Offer opportunities to match problems to bar models, ensure the same numbers are used to highlight the differences.
Pose the question 'Can all values be divided in a ratio?' Give an example, maybe share 10 in the ratio 1:3, then introduce various contexts and reconsider if it is possible. Other questions could be 'how 'many' do a need to add so that I can?'.
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
6 Questions
Q1.Which of the following are terminating decimals?
Which of the following are terminating decimals?
$$15.\dot4$$
Correct answer: 15.44449
15.44449
Correct answer: 15.000085
15.000085
$$2\over3$$
Correct answer: 15.021568652
15.021568652
Q2.Match each calculation to the correct missing number.
Match each calculation to the correct missing number.
Correct Answer:9 × $$\square$$ = 4,$$4\over9$$
9 × $$\square$$ = 4 - $$4\over9$$
Correct Answer:$$\square$$ × 9 = $$3\over2$$,$$1\over6$$
$$\square$$ × 9 = $$3\over2$$ - $$1\over6$$
Correct Answer:9 × $$\square$$ = 12,$$4\over3$$
9 × $$\square$$ = 12 - $$4\over3$$
Correct Answer:9 × $$\square$$ = 22.5,2.5
9 × $$\square$$ = 22.5 - 2.5
Correct Answer:$$\square$$ × 9 = $$1\over3$$,$$1\over27$$
$$\square$$ × 9 = $$1\over3$$ - $$1\over27$$
Q3.A recipe requires 195 grams of chocolate chips to bake 30 cookies. What weight of chocolate chips would you need to make 500 cookies? Give your answer in grams.
A recipe requires 195 grams of chocolate chips to bake 30 cookies. What weight of chocolate chips would you need to make 500 cookies? Give your answer in grams.
Correct Answer: 3250 g, 3250 grams, 3250g, 3250grams, 3250
3250 g, 3250 grams, 3250g, 3250grams, 3250
Q4.What fraction of 180 is 55? Give your answer in its simplest form.
What fraction of 180 is 55? Give your answer in its simplest form.
Correct answer: $$11\over36$$
$$11\over36$$
$$25\over36$$
$$55\over180$$
$$125\over180$$
$$180\over55$$
Q5.If 525 is $$3\over5$$ of 875, which of the following is true?
If 525 is $$3\over5$$ of 875, which of the following is true?
875 is $$3\over3$$ of 525
875 is $$3\over5$$ of 525
525 is $$5\over3$$ of 875
Correct answer: 875 is $$5\over3$$ of 525
875 is $$5\over3$$ of 525
Q6.Match the following with what needs to go in the box.
Match the following with what needs to go in the box.
Correct Answer:130 is $$\square$$ of 104,$$5\over4$$
130 is $$\square$$ of 104 - $$5\over4$$
Correct Answer:$$\square$$ of 228 is 304 ,$$4\over3$$
$$\square$$ of 228 is 304 - $$4\over3$$
Correct Answer:412 is $$\square$$ of 515,$$4\over5$$
412 is $$\square$$ of 515 - $$4\over5$$
Correct Answer:$$\square$$ of 964 is 723,$$3\over4$$
$$\square$$ of 964 is 723 - $$3\over4$$
Correct Answer:1209 is $$\square$$ of 2015,$$3\over5$$
1209 is $$\square$$ of 2015 - $$3\over5$$
Assessment exit quiz
6 Questions
Q1.Fill in the missing word: Variables are in proportion if they have a constant relationship.
Fill in the missing word: Variables are in proportion if they have a constant relationship.
Correct Answer: multiplicative, multiplication, multiply, times , ×
multiplicative, multiplication, multiply, times , ×
Q2.Share 75 in the ratio 2 : 3. Which is a correct first step in solving this problem?
Share 75 in the ratio 2 : 3. Which is a correct first step in solving this problem?
75 ÷ 2
75 ÷ 3
75 ÷ 4
Correct answer: 75 ÷ 5
75 ÷ 5
75 ÷ 6
Q3.Alex and Lucas share 75 sweets in the ratio of 2 : 3. How many sweets does Lucas get?
Alex and Lucas share 75 sweets in the ratio of 2 : 3. How many sweets does Lucas get?
Correct Answer: 45, forty-five, forty five, fortyfive
45, forty-five, forty five, fortyfive
Q4.Share 96 in the ratio 2 : 7 : 3. What is the value of the largest share?
Share 96 in the ratio 2 : 7 : 3. What is the value of the largest share?
Correct Answer: 56, fifty-six, fifty six, fiftysix
56, fifty-six, fifty six, fiftysix
Q5.The ratio of flour to butter to sugar in a cookie recipe is 3 : 2 : 1. You want to make a giant cookie weighing 720 grams. How much butter will you need?
The ratio of flour to butter to sugar in a cookie recipe is 3 : 2 : 1. You want to make a giant cookie weighing 720 grams. How much butter will you need?
Correct Answer: 240 g, 240 grams, 240g, 240grams, 240
240 g, 240 grams, 240g, 240grams, 240
Q6.The perimeter of a triangle is 48 cm. The sides are in the ratio 7:5:8. How long is the shortest side?
The perimeter of a triangle is 48 cm. The sides are in the ratio 7:5:8. How long is the shortest side?
Correct Answer: 12 cm, 12cm, 12 centimetres, 12 centimetre, 12
12 cm, 12cm, 12 centimetres, 12 centimetre, 12
