Math · Unit 10

Ratio, Proportion and Percent

Ratios, rates, proportions, percent problems and scale

Proportional reasoning is the single most useful mathematical skill outside a classroom - recipes, maps, exchange rates, discounts and scale drawings are all one idea.

The unit covers ratios, rates and unit rates, setting up and solving proportions, percentage problems in both directions, and scale.

This unit breaks down into 21 short steps and 120 questions, starting at difficulty 3 and building to 4. Below you can see exactly what it covers, how the path is structured, and worked examples with explanations.

Steps: 21
Questions: 120
Difficulty: 3-4

What this unit covers

Ratios
Proportions
Rates and Unit Rates
Percent Problems
Scale and Maps

Where this fits

Needs Fractions and Decimals. Used constantly in Probability and Statistics and in the sciences.

Where people slip

A percentage increase followed by the same percentage decrease does not return you to the start. Up twenty then down twenty leaves you at ninety-six per cent of where you began.

How the unit is structured

Ratio, Proportion and Percent runs as 21 short steps that unlock in order. 15 are practice rounds and 6 are challenge rounds that pull together everything before them. Questions start at difficulty 3 and climb to 4 as you progress.

Step 1 · easierStep 21 · harder

Challenge rounds

Example questions

30 real questions from this unit, with the answer and the reason behind it, grouped by what they practise. There are 120 in the unit altogether.

Percent Problems

Build the sentenceLevel 3
1. Build a true sentence about percents.
Answer: Fifty percent is the same as one half
Fifty percent is the same as one half.
Fact or fibLevel 3
2. 10% of 200 is 20.
Answer: True
10% means one tenth, and 200 / 10 = 20.
Fill the blankLevel 3
3. Percent means per ____.
- hundredcorrect
- ten
- thousand
- dozen
Percent comes from 'per hundred', so 25% means 25 per 100.
Match the pairsLevel 3
4. Match each percent to the fraction that equals it.
Answer: 50% = 1/2; 25% = 1/4; 20% = 1/5
50% is 1/2, 25% is 1/4, and 20% is 1/5.
Multiple choiceLevel 3
5. What is 25% of 80?
- 20correct
- 25
- 16
- 40
25% is 1/4, and 80 / 4 = 20.
Guess the numberLevel 4
6. An $80 item is discounted 35%. What is the sale price in dollars?
Answer: 52 dollars
You pay 65% of 80, and 0.65 x 80 = 52.

Proportions

Fact or fibLevel 3
7. The proportion 1/2 = 4/8 is true.
Answer: True
4/8 simplifies to 1/2, so the two ratios are equal.
Fill the blankLevel 3
8. A proportion is an equation stating that two ____ are equal.
- ratioscorrect
- sums
- products
- remainders
A proportion sets two equal ratios equal to each other.
Guess the numberLevel 3
9. Solve the proportion 5/8 = x/40. What is x?
Answer: 25
40 is 8 times 5, so x is 5 times 5, which is 25.
Multiple choiceLevel 3
10. Solve the proportion 3/4 = x/12.
- 9correct
- 16
- 8
- 12
Since 12 is 4 times 3, x is 3 times 3, which is 9.
Odd one outLevel 3
11. Which proportion is NOT true?
- 2/3 = 5/7correct
- 1/2 = 3/6
- 2/4 = 5/10
- 3/5 = 6/10
2/3 = 5/7 is false because 2 x 7 = 14 but 3 x 5 = 15; the others are true.
Choose all that applyLevel 4
12. Which pairs of ratios form a true proportion? Select all that apply.
- 1/3 and 4/12correct
- 2/5 and 6/15correct
- 3/4 and 9/16
- 5/6 and 10/12correct
1/3 = 4/12, 2/5 = 6/15 and 5/6 = 10/12 are true; 3/4 does not equal 9/16.

Rates and Unit Rates

Build the sentenceLevel 3
13. Build a true sentence about unit rates.
Answer: Unit rate has a denominator of one
A unit rate compares an amount to a single unit, so its denominator is one.
Fact or fibLevel 3
14. A car going 60 miles per hour travels 120 miles in 2 hours.
Answer: True
60 miles each hour for 2 hours is 60 x 2 = 120 miles.
Fill the blankLevel 3
15. A ____ rate has a denominator of 1.
- unitcorrect
- double
- half
- percent
A unit rate compares an amount to just one unit, so its denominator is 1.
Match the pairsLevel 3
16. Match each situation to its unit rate.
Answer: 120 miles in 2 hours = 60 mph; $10 for 5 lb = $2 per lb; 90 words in 3 min = 30 wpm
120 miles in 2 hours is 60 mph, $10 for 5 lb is $2 per lb, and 90 words in 3 min is 30 wpm.
Multiple choiceLevel 3
17. 12 apples cost $6. What is the price per apple?
- $0.50correct
- $2
- $0.60
- $1
6 / 12 = 0.50, so each apple costs $0.50.
Choose all that applyLevel 4
18. Which of these give a unit rate of 5 km per hour? Select all that apply.
- 10 km in 2 hourscorrect
- 15 km in 3 hourscorrect
- 20 km in 5 hours
- 25 km in 5 hourscorrect
10 km in 2 h, 15 km in 3 h and 25 km in 5 h all equal 5 km/h; 20 km in 5 h is only 4 km/h.

Ratios

Build the sentenceLevel 3
19. Build a true sentence about ratios.
Answer: A ratio compares two quantities
A ratio is a comparison of two quantities.
Choose all that applyLevel 3
20. Which of these ratios are equivalent to 2:3? Select all that apply.
- 4:6correct
- 6:9correct
- 2:5
- 3:2
4:6 and 6:9 both simplify to 2:3; 2:5 and 3:2 do not.
Fill the blankLevel 3
21. A ratio compares two ____.
- quantitiescorrect
- colors
- shapes
- letters
A ratio is a comparison of two quantities.
Match the pairsLevel 3
22. Match each ratio to its simplest form.
Answer: 6:8 = 3:4; 10:15 = 2:3; 8:20 = 2:5
6:8 reduces to 3:4, 10:15 reduces to 2:3, and 8:20 reduces to 2:5.
Multiple choiceLevel 3
23. Simplify the ratio 8:12 to its lowest terms.
- 2:3correct
- 3:2
- 1:2
- 3:4
Both 8 and 12 divide by 4, giving 2:3.
Odd one outLevel 3
24. Which ratio is NOT equivalent to 1:2?
- 3:5correct
- 2:4
- 4:8
- 5:10
3:5 is not equal to 1:2, while 2:4, 4:8 and 5:10 all simplify to 1:2.

Scale and Maps

Build the sentenceLevel 3
25. Build a true sentence about map scales.
Answer: Map scale relates distances to real life
A map scale relates the distances on a map to distances in real life.
Choose all that applyLevel 3
26. Which of these represent a scale of 1:100? Select all that apply.
- 1 cm : 100 cmcorrect
- 1 cm : 1 mcorrect
- 2 cm : 200 cmcorrect
- 1 cm : 10 cm
1 cm : 100 cm, 1 cm : 1 m (100 cm) and 2 cm : 200 cm are all 1:100; 1 cm : 10 cm is 1:10.
Fact or fibLevel 3
27. On a map with scale 1:100, 1 cm represents 100 cm in real life.
Answer: True
A scale of 1:100 means every 1 unit on the map is 100 units in real life.
Fill the blankLevel 3
28. The ____ factor tells how many times larger or smaller a drawing is than the real object.
- scalecorrect
- unit
- percent
- place
The scale factor is the ratio of drawing size to real size.
Match the pairsLevel 3
29. A map uses a scale of 1 cm : 20 km. Match each map length to its real distance.
Answer: 2 cm = 40 km; 5 cm = 100 km; 8 cm = 160 km
Multiply each map length by 20 km to get 40, 100 and 160 km.
Multiple choiceLevel 3
30. A model car is built at a scale of 1:20. The model is 10 cm long. How long is the real car?
- 200 cmcorrect
- 2 cm
- 30 cm
- 100 cm
The real car is 20 times the model, so 10 x 20 = 200 cm.

Where these questions come from. Each unit starts as a plan of the concepts it should cover and the difficulty it should span. Questions are written against that plan with AI assistance, then checked by a validator that rejects anything without a single defensible answer, an explanation, or plausible wrong options. How we write questions sets out the whole process, and corrections are fixed in the bank and reach the site and the app the same day.

How you practise

This unit mixes 14 different question formats, so you are recalling and applying rather than recognising the same layout every time.

Build the sentence
Choose all that apply
Fact or fib
Fill the blank
Guess the number
Match the pairs
Multiple choice
Odd one out
Picture question
Put in order
Sort into groups
Spell it
True or false
Type the answer

Practise Ratio, Proportion and Percent

120 questions across 21 steps. Start with step one and crawl at your own pace.

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Read about Ratio, Proportion and Percent

Explainers from our blog on what this unit covers. Each one ends with real questions from the bank.

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