• Free
  • Grade 8
  • Equation vs table or words

Which rate is greater? worksheets

Which one is faster? These free printable worksheets put an equation next to a table or a written rate and ask which has the greater rate.

Kid stuck on one? You don’t just get the sheet.

  • Answer key included
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Ready to printWhich rate is greater?
Which rate is greater? worksheet — Equation vs table or words, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The bigger number on the page is often the wrong answer, and that is the whole sheet. Put y = 7x next to “45 km in 9 hours” and a student who compares what is written picks the 45. It is 5 km per hour, and it loses. Nothing on the page can be compared until both sides have been turned into the same kind of number, and turning each one into a rate PER ONE is the only work there is here.

Why this sheet works

So every page carries questions where the bigger printed number belongs to the slower one, drawn from a stratum of their own rather than left to luck. A sheet where the bigger number always wins can be cleared by reading instead of by dividing, which is exactly what this standard exists to stop.

How this one works

One question from this sheet, worked through a step at a time.

A x: 4, 7, 10 y: 60, 105, 150 B y = 3x, y words and x minutes

Ax: 4, 7, 10 y: 60, 105, 150
By = 3x, y words and x minutes
60 ÷ 4=15 per minute
y = 3x, y words and x minutes3 per minute
A 15B 3
greater:A
  1. These two are written in different ways, so there is nothing to compare yet — the numbers on the page are not the same kind of number. Turn each one into a rate PER ONE minute first, and do not look at which looks bigger until you have.
  2. A: any column divided by its own x — 60 ÷ 4 = 15. So A is 15 words per minute.
  3. B: the number in front of x, which is already a rate per one minute: 3. So B is 3 words per minute.
  4. Now they can be compared: A is 15 and B is 3 per minute, so A is greater.