Rewriting Expressions to Reveal Relationships Worksheets, Grade 7 (7.EE.A.2) – Free PDF + Answer Key

First page of the rewriting expressions to reveal relationships 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

Increase by p%: multiply by 1 + p/100. Decrease by p%: multiply by 1 − p/100. Writing a change as a single multiplier lets you chain changes by multiplying the factors together.

Sample problems

Write “x increased by 10%” as a single multiplication.
Find the result when x = 300.
Write “x decreased by 15%” as a single multiplication.
Find the result when x = 200.

Common mistakes to watch for

Wrote 0.05x alone, which is just the increase and not the new price. The original has to stay in.
Wrote 0.2x, which is the amount removed rather than what remains. 100% − 20% = 80% is what is left.
Said they are the same so it does not matter. They are equal in value and different in what they communicate, and choosing the informative one is the skill.

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.