Ratios
Ratios from pictures
Count two kinds of shapes in four picture arrays. Write and simplify part-to-part ratios, with an optional second question comparing one group with the whole.
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Ratio and rate worksheets
Compare quantities, keep their order, and explain the relationship. Start with pictures, build equivalent ratios, then put unit rates to work.
Choose a ratio skill3 : 2Multiply both quantities by 2
6 : 4
Blue circles : amber circles
Compare, scale, explain
Read and represent ratios
Connect counted shapes and verbal comparisons with an ordered ratio. Distinguish a part from the whole before simplifying.
Ratios
Write ratios from word phrases
Turn twenty word phrases into fractions in simplest form. Practice ordered comparisons and distinguish “to” from “out of” a stated total.
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Build equivalent relationships
Scale both quantities together, complete missing terms and identify matching ratios in contextual tables.
Ratios
Complete rows of equivalent ratios
Fill missing terms in ten rows of six equivalent ratios. Choose consecutive or gapped scale factors and ordered or shuffled practice, with printable answer keys.
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Ratios
Equivalent ratios: tables, comparisons and missing values
Practice eighteen equivalent-ratio questions in three formats: complete ratio tables, decide whether pairs are equivalent, and solve missing-value proportions.
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Ratios
Find equivalent ratios in tables
Compare four named rows of data and identify the two with equivalent ratios. Choose three contextual problems or a six-problem set, with separate answer pages.
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Find rates and solve problems
Express a quantity per one unit, compare offers and use constant rates to scale a result.
Ratios
Rates and unit rates
Write a labeled rate and calculate a unit rate for ten word phrases. Keep the units in order and round the final unit rate to two decimal places.
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Ratios
Mixed ratios and unit rates
Combine eight simplest-form ratio questions with eight rate and unit-rate questions. Practice choosing the correct representation and keeping units with every answer.
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Ratios
Ratio and rate word problems
Solve seven contextual problems using constant rates, time conversions, fuel use and better-buy comparisons. Answer linked scaling and unit-rate questions with separate worked keys.
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Start with a relationship the learner can describe
Picture comparisons work well after array counting and common factors are familiar. Move to rates and proportions when learners can explain equivalent fractions and division. These starting points describe readiness, not alignment with a particular country's curriculum.
Describe two counted groups
A teacher-led introduction after array counting and common factors are secure. Begin with the part-to-part comparison only.
Open this focused practice →Use the ratio, not the sequence
Gaps and shuffled positions require learners to derive each missing value from the complete anchor.
Open this focused practice →Apply constant rates and compare prices
Use after unit rates and time conversions are familiar. Keep exact intermediate values and answer every part.
Open this focused practice →A ratio has an order
If a box contains 6 blue counters and 9 amber counters, blue to amber is 6:9, or 2:3. Amber to blue is 9:6, or 3:2. Those are different comparisons.
Amber to all counters is 9:15, or 3:5, because there are 15 counters altogether. Naming both quantities before calculating helps prevent part-to-part and part-to-whole confusion.
Equivalent ratios scale both quantities together
Build
2:5 becomes 4:10 when both quantities double. Tripling both gives 6:15.
Check
3:4 and 9:12 are equivalent: both terms have been multiplied by 3. Their cross-products also match.
Complete
For 3:4 = 15:x, the first quantity is multiplied by 5. The second must be 4 × 5, so x = 20.
Ordered rows reveal a pattern. Gaps and shuffling test whether students understand the relationship independently of the order in which the ratios appear.
A unit rate describes one unit
If a cyclist travels 42 kilometres in 3 hours at a constant rate, the rate is 42 kilometres per 3 hours. Dividing gives a unit rate of 14 kilometres per hour.
Reversing the division answers a different question: 3/42 hours per kilometre. Keep the units beside the quantities so the answer matches what was asked.
The unit-rate sheets request two decimal places. Keep the exact quotient until the final rounding step, and include the unit phrase with the result.
Read every part of an application problem
A problem can ask both for a scaled amount and for the unit rate. For a machine that handles 45 items in 15 minutes, first convert to a common time unit: that is 180 items per hour. At the same rate, two hours gives 360 items.
Use exact values for intermediate work. Rounding a rate before multiplying can change the final answer. When comparing prices, compare exact unit costs so a rounded tie does not hide the cheaper offer.
Print a focused lesson or mixed practice
All eight activities include free English PDFs, image previews and answer keys. Choose Letter or A4. The table activity offers three problems or six across two student pages; longer notes or translated text may require extra space.
Use the online generator to make a fresh set or save the configured link for the same questions later. Changing paper or printed language preserves the mathematics.