Comparing rates

Use the same unit before choosing.

Use the same unit before choosing.

Compare on a common basis

To compare prices, calculate cost per the same unit: dollars per kilogram, not dollars per 100 g for one package and dollars per kilogram for another.

Make a prediction · test a relationship

See the quantities change.

Predict before changing a value. The written explanation below remains available without JavaScript.

Decide what better means

Lower cost per kilogram is cheaper; higher pages per minute is faster. Compare the right direction and interpret it in context. A larger package is not automatically cheaper.

Keep precision until the decision

Use unrounded unit rates to decide which is lower. Round the displayed price appropriately afterward. A better unit price is not the only consideration: needed quantity, quality and waste may matter.

Khan Academy

Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.

Follow the reasoning

Worked examples

Which has the lower unit price: 750 g for $4.50 or 1.2 kg for $6.60?

  1. Convert 750 g to 0.75 kg.
  2. A: 4.50 ÷ 0.75 = $6.00/kg. B: 6.60 ÷ 1.2 = $5.50/kg.
  3. B costs $0.50 less per kilogram.

Printer A makes 84 pages in 4 min. B makes 115 pages in 5 min.

  1. A: 84 ÷ 4 = 21 pages/min.
  2. B: 115 ÷ 5 = 23 pages/min.
  3. B is faster on these average rates.

Try it before checking.

A costs $8 for 2 kg; B costs $15 for 3 kg. Which costs less per kilogram?

A first hint

Find dollars per kilogram for each.

Compare your reasoning

A is $4/kg; B is $5/kg. A has the lower unit price.

Practise the skill.

Fresh questions · useful feedback

Build fluency, one decision at a time.

Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.

0 of 8 questions completed

Enter a number, decimal or fraction such as −3/2. Include the sign; leave out units.

This round saves on this device. It is practice, not a school mark.

Explain a little more.

Give a situation where the better unit price would still be a poor purchase.

Use this thinking in the If… project →

Keep the connections going.

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