Year 8 in England
7th grade ratio and proportion
16 7th grade ratio and proportion skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.
Mixed review
Ten questions drawn from every skill below.
Proportional relationships
CCSS 7.RP.A.2CCSS 7.RP.A.3England: KS3 RatioEngland: GCSE Foundation Ratio
Example
Is this relationship proportional? x: 3, 8, 10 → y: 27, 72, 90
- 27 ÷ 3 = 9 ; 72 ÷ 8 = 9 ; 90 ÷ 10 = 9
- Always 9: proportional.
Answer: Yes, proportional
Scale drawings and maps
CCSS 7.G.A.1England: KS3 RatioEngland: GCSE Foundation Ratio
Example
On a map, 1 cm represents 20 km. Two towns are 15 cm apart on the map. How far apart are they really, in km?
- 15 × 20 = 300 km
Answer: 300
Builds on: Proportional relationships
Leads to: Scale factors and enlargement, Use a scale to find real lengths
Unit rates with fractions (complex fractions)
CCSS 7.RP.A.1England: KS3 Ratio, proportion and rates of change
Example
Felix walks 3/2 mile in 1/6 hour. What is Felix's speed in miles per hour? Give a whole number, fraction or mixed number.
- 3/2 ÷ 1/6 = 3/2 × 6/1 = 18/2
- = 9 mph
Answer: 9
Builds on: Unit rates, Divide fractions by fractions
Decide if a table shows a proportional relationship
CCSS 7.RP.A.2.AEngland: KS3 Ratio, proportion and rates of change
Example
Hours worked (x): 1, 5, 7, 9. Pay (y): 6, 30, 42, 54. Is y proportional to x?
- 6 ÷ 1 = 6, 30 ÷ 5 = 6, 42 ÷ 7 = 6, 54 ÷ 9 = 6
- Always the same: proportional.
Answer: Yes
Builds on: Proportional relationships
Find the constant of proportionality from a table
CCSS 7.RP.A.2.BEngland: KS3 Ratio, proportion and rates of change
Example
Number of tickets (x): 6, 7, 10. Cost (y): 66, 77, 110. What is the constant of proportionality k (y = kx)?
- 66 ÷ 6 = 11
Answer: 11
Find the constant of proportionality from a graph
CCSS 7.RP.A.2.BCCSS 7.RP.A.2.DEngland: KS3 Ratio, proportion and rates of change
Decide if a graph shows a proportional relationship
CCSS 7.RP.A.2.AEngland: KS3 Ratio, proportion and rates of change
Example
Which situation gives a proportional relationship between cost and amount?
- Only the apples have no fixed fee, so cost = rate × amount.
Answer: Apples: $6 per kg, nothing else
Write equations for proportional relationships
CCSS 7.RP.A.2.CEngland: KS3 Ratio, proportion and rates of changeEngland: KS3 Algebra
Example
Each streaming song earns 13 points. Write an equation for y in terms of s. Type only the right-hand side (y = …).
- y = 13s
Answer: 13s
Solve proportions
CCSS 7.RP.A.2CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
Solve: x / 9 = 4 / 3
- 3 × 3 = 9
- x = 4 × 3 = 12
Answer: x = 12
Builds on: Proportional relationships
Leads to: Solve real-world proportion problems
Solve real-world proportion problems
CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
A pancake recipe for 4 people uses 360 g of flour. How much flour is needed for 9 people, in grams?
- 360 ÷ 4 = 90 g
- 90 × 9 = 810 g
Answer: 810
Builds on: Solve proportions
Use a scale to find real lengths
CCSS 7.G.A.1England: KS3 Ratio, proportion and rates of changeEngland: KS3 Geometry and measures
Example
On a map, 1 cm represents 20 km. Two towns are 15.5 cm apart on the map. How far apart are they really, in km?
- 15.5 × 20 = 310 km
Answer: 310
Builds on: Scale drawings and maps
Find drawing lengths and the scale of a drawing
CCSS 7.G.A.1England: KS3 Ratio, proportion and rates of changeEngland: KS3 Geometry and measures
Example
A model uses 1 cm for every 2 m. A real bridge is 6 m long. How long is it on the model, in cm?
- 6 ÷ 2 = 3 cm
Answer: 3
Builds on: Use a scale to find real lengths
Leads to: Areas in scale drawings
Areas in scale drawings
CCSS 7.G.A.1England: KS3 Ratio, proportion and rates of changeEngland: KS3 Geometry and measures
Example
A rectangle on a plan is 8 cm by 3 cm. The scale is 1 cm : 2 m. What is the real area, in m²?
- 8 × 2 = 16 m, 3 × 2 = 6 m
- 16 × 6 = 96 m²
Answer: 96
Connect ratios and fractions
CCSS 7.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
Juice and water are mixed in the ratio 6:8. What fraction of the drink is juice? Give a fraction in simplest form.
- 6/14 = 3/7
Answer: 3/7
Builds on: Understand ratios
Keep exploring
7th grade topic pages
More for 7th grade
Hands-on math tools
- Virtual fraction bars and fraction circles
- Interactive number line
- Virtual base ten blocks
- Multiplication arrays
- Interactive teaching clock
- Virtual money for counting practice
- Interactive coordinate plane
- Algebra balance scale
- Adding fractions with a model
- Virtual algebra tiles
- Alphabetical order game
- Virtual protractor and angle maker
- Area and perimeter builder
- Bar graph maker for kids
- Math by topicFractions, times tables, long division and more
- English and grammarNouns, verbs, commas, spelling and more
- Reading passagesShort stories with read-aloud and questions
- Science by gradePlants, forces, matter, space and more
- Printable worksheetsPrint, or do them on a tablet with a finger or pen
- Free math games3D games where every move is a math question
- Manipulatives and simulationsMath tools plus science sims: cells, atoms, forces, planets
- Fraction calculatorEvery step shown, from mixed numbers to simplest form
- Math 5-a-dayFive fresh warm-up questions every day
- Guides for parentsHow to help with fractions, tables, tests and more
Math, English and science that click.