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Year 10
Higher

Writing equations from ratios

I can write equations involving ratios.

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New
New
Year 10
Higher

Writing equations from ratios

I can write equations involving ratios.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Ratios can be written as fractions.
  2. A ratio can be used to write an equation.
  3. This equation is another way of representing how the two quantities are connected.
  4. Either of the quantities can be the subject.

Common misconception

When $$x : y$$ are in the ratio 1 : 2 pupils write the equation as $$x = 2y$$

The bar models shown in this lesson can help to support pupils with this.

Keywords

  • 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.

  • Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.

  • Equation - An equation is used to show 2 expressions that are equal to each other.

Linking the equation to the multiplier in a ratio table can further prevent the misconception that $$x : y$$ in the ratio 1 : 2 is written as $$x = 2y$$ because in a ratio table this would mean the multiplier from y to x would be times by 2, this would mean when y=1 x=2 which is 2 : 1 not 1 : 2
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Which of the following is the correct way of writing the ratio 1 to 2?
1 ; 2
Correct answer: 1 : 2
1 - 2
1 , 2
1 . 2
Q2.
There are 36 cans of drink and bags of sweets in a vending machine. The ratio of cans : bags is 2 : 1. 4 of each are sold. What is the ratio of cans : bags now? (In its simplest form)
Correct Answer: 5 : 2, 5:2
Q3.
There are 56 vehicles in a car park. The ratio of cars : vans is 5 : 2. 4 more vans enter the car park. What is the ratio of cars : vans now? (Give your answer in its simplest form)
Correct Answer: 2 : 1, 2:1
Q4.
The ratio of adults to children at an athletics club is 8 : 5. 8 adults leave, the ratio is now 4 : 3. How many children are members of the club?
Correct Answer: 30 , 30 children
Q5.
3 bags contain counters in the ratio 6 : 3 : 5. Some counters are taken out of 1 bag and put into the other 2. The ratio of counters is now 6 : 5 : 10. What is the minimum number of counters removed?
Correct Answer: 6 , 6 counters, six , six counters
Q6.
The ratio of the number of £1 coins to £2 in Sam’s money box is 3 : 2. Their gran gives them 6 more £1 coins, the ratio is now 2 : 1. How much money was in Sam’s money box originally?
£11
£13
£30
Correct answer: £42
£48

Exit quiz

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6 Questions

Q1.
The 3 in $$3a$$ is the .
number
expression
Correct answer: coefficient
unknown
term
Q2.
What is the equation of $$y$$ in terms of $$x$$?
An image in a quiz
$$y=6x$$
$$y={1\over5}x$$
Correct answer: $$y=5x$$
$$y={1\over6}x$$
Q3.
What is the equation of $$y$$ in terms of $$x$$?
An image in a quiz
$$y={1\over2}x$$
$$y=2x$$
Correct answer: $$y={1\over3}x$$
$$y=3x$$
Q4.
Match each ratio of $$x$$ : $$y$$ to the correct equation of $$y$$ in terms of $$x$$.
Correct Answer:1 : 4,$$y=4x$$

$$y=4x$$

Correct Answer:4 : 1,$$y={1\over4}x$$

$$y={1\over4}x$$

Correct Answer:3 : 2,$$y={2\over3}x$$

$$y={2\over3}x$$

Correct Answer:2 : 3,$$y=1.5x$$

$$y=1.5x$$

Correct Answer:3 : 5,$$y={5\over3}x$$

$$y={5\over3}x$$

Q5.
The ratio of adults to children at a running club is 7 : 5. Which of the following are correct equations linking adults and children?
$$a={5\over7}c$$
$$c={7\over5}a$$
Correct answer: $$c={5\over7}a$$
Correct answer: $$a={7\over5}c$$
Q6.
$$8x-2y = 3x+5y$$. What is the ratio of $$x:y$$?
Correct Answer: 7 : 5, 7:5