Year 7 in England
6th grade ratio and proportion
10 6th 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.
Understand ratios
CCSS 6.RP.A.1England: Y6 Ratio and proportionEngland: KS3 Ratio
Example
Simplify the ratio 18:12. Type it like 3:2.
- Divide both parts by 6.
- 18:12 = 3:2
Answer: 3:2
Unit rates
CCSS 6.RP.A.2CCSS 6.RP.A.3.BEngland: Y6 Ratio and proportionEngland: KS3 RatioEngland: GCSE Foundation Ratio
Example
7 notebooks cost $63. What is the cost of one notebook? (Type the number only.)
- 63 ÷ 7 = 9
Answer: 9
Ratio tables and double number lines
CCSS 6.RP.A.3.AEngland: Y6 Ratio and proportionEngland: KS3 Ratio
Example
A recipe uses 5 eggs for every 5 pancakes. Complete the table: eggs 5, 10, 25; pancakes 5, 10, __
- 25 ÷ 5 = 5
- 5 × 5 = 25
Answer: 25
Write part-to-part and part-to-whole ratios
CCSS 6.RP.A.1England: Y6 Ratio and proportionEngland: KS3 Ratio, proportion and rates of change
Example
A playlist has 9 pop songs, 12 rock songs and 3 jazz songs. Write the ratio pop : rock : jazz in simplest form (like 1:2:3).
- 9:12:3
- = 3:4:1
Answer: 3:4:1
Builds on: Understand ratios
Decide whether ratios are equivalent
CCSS 6.RP.A.3.AEngland: KS3 Ratio, proportion and rates of change
Example
Are the ratios 1:3 and 5:14 equivalent?
- 1 × 5 = 5
- 3 × 5 = 15
- 15 ≠ 14, so they are not equivalent.
Answer: No
Builds on: Understand ratios
Leads to: Use a ratio to find a missing quantity
Complete ratio tables
CCSS 6.RP.A.3.AEngland: KS3 Ratio, proportion and rates of change
Example
Complete the ratio table. Laps run: 2, 4, 10, 14. Minutes: 4, 8, 20, ?
- 14 ÷ 2 = 7
- 4 × 7 = 28
Answer: 28
Builds on: Ratio tables and double number lines
Use a ratio to find a missing quantity
CCSS 6.RP.A.3England: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
The ratio of goals to missed shots is 4:5. There are 32 goals. How many missed shots are there?
- One part = 32 ÷ 4 = 8
- 5 × 8 = 40
Answer: 40
Builds on: Decide whether ratios are equivalent
Work out unit prices
CCSS 6.RP.A.2CCSS 6.RP.A.3.BEngland: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
4 notebooks cost $3.16. What is the price for 1? (Type the number only.)
- 3.16 ÷ 4 = 0.79
Answer: 0.79
Builds on: Unit rates, Divide decimals
Leads to: Compare deals to find the better value
Compare deals to find the better value
CCSS 6.RP.A.3.BEngland: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
Pack A: 6 cans of sparkling water for $4.02. Pack B: 8 cans of sparkling water for $4.96. Which pack is better value?
- A: $4.02 ÷ 6 = $0.67
- B: $4.96 ÷ 8 = $0.62
- Pack B is better value.
Answer: Pack B
Builds on: Work out unit prices
Solve constant-rate problems: speed, work and data
CCSS 6.RP.A.3.BEngland: KS3 Ratio, proportion and rates of changeEngland: GCSE Foundation Ratio
Example
Isla cycles 46 km in 2 hours at a steady speed. How far will Isla cycle in 7 hours at the same speed, in km?
- 46 ÷ 2 = 23 km/h
- 23 × 7 = 161 km
Answer: 161
Builds on: Unit rates
Keep exploring
6th grade topic pages
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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.