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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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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Read every part of each problem. Keep exact intermediate values, use consistent time units, and label your answers. Round numerical results to the requested whole unit; compare prices using exact unit costs.
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Learning objective
What this activity builds
Use proportional reasoning to scale a quantity, compare unit prices and explain a rate in context.
Worked example
A machine labels 45 boxes in 15 minutes. At that constant rate, how many boxes can it label in two hours, and how many per hour?
360 boxes in two hours; 180 boxes per hour.
There are four 15-minute intervals in an hour, so the hourly rate is 45 × 4 = 180 boxes. Two hours then gives 180 × 2 = 360. Both answers depend on the same unchanged rate.
Teaching notes
Make the practice count
- Identify all requested outputs before calculating; several questions have two parts.
- Convert time units before scaling a rate.
- Compute each unit price exactly when comparing offers; rounding can hide a real difference.
- For rounded final answers, retain the exact intermediate quotient when calculating a later quantity.
- Use the answer key to discuss the method as well as the result.
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