Multi-Step Ratio Problems Worksheets, Grade 7 (7.RP.A.3) – Free PDF + Answer Key

First page of the multi-step ratio problems practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Two reliable routes. Unit rate: find the value of one, then multiply. Scale factor: find what the quantity was multiplied by, then multiply the other by the same. For a ratio sharing a total, add the parts first to find what one part is worth.

Sample problems

2 pens cost $3. What do 8 pens cost?
5 metres of rope cost $40. What does 1 metre cost?
Using that, what do 9 metres cost?
A machine packs 7 kg in 21 minutes. How long for 10 kg?

Common mistakes to watch for

Answered $14 by adding 2 books and $2. That makes each book cost $2.80 instead of $4 — the price changed, so the ratio is broken.
Answered 13 by adding 9 to both. Adding the same amount to each side changes the ratio.
Multiplied only one part, giving 6 : 5 or 2 : 15. Both parts scale, or the mixture changes.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.