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Fractions, decimals and percentsGrade 7

Percent change worksheet with answer key

A seventh-grade generator for percent of change. Each line gives an original and a new amount, and the student writes the percent and whether it is an increase or decrease. Other percent skills are one menu away.

By Paul Gunder. Free to print for home, classroom and office use; see how our printables are made.

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Percent of Change2 pages, answer key from page 2 · US Letter

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NameDateScorePercent of ChangeFind the percent of change and write increase or decrease. Percent of change = (new − original) ÷ original × 100.1.From 160 to 152: 2.From 80 to 32: 3.From 400 to 640: 4.From 120 to 144: 5.From 80 to 112: 6.From 400 to 80: 7.From 20 to 36: 8.From 500 to 400: 9.From 500 to 1250: 10.From 240 to 192: 11.From 60 to 30: 12.From 100 to 90: 13.From 60 to 63: 14.From 200 to 150: 15.From 60 to 36: 16.From 120 to 24: PrintablePal.com · free printablesPercent of Change
Worksheet, page 1
Percent of Change: answer key1.From 160 to 152: 5% decrease2.From 80 to 32: 60% decrease3.From 400 to 640: 60% increase4.From 120 to 144: 20% increase5.From 80 to 112: 40% increase6.From 400 to 80: 80% decrease7.From 20 to 36: 80% increase8.From 500 to 400: 20% decrease9.From 500 to 1250: 150% increase10.From 240 to 192: 20% decrease11.From 60 to 30: 50% decrease12.From 100 to 90: 10% decrease13.From 60 to 63: 5% increase14.From 200 to 150: 25% decrease15.From 60 to 36: 40% decrease16.From 120 to 24: 80% decreasePrintablePal.com · free printablesAnswer key
Answer key, page 1

On this page

The idea behind percent of change

Percent of change answers one question: compared with where it started, how much did a quantity grow or shrink? A jacket that goes from $40 to $50 has changed by $10, but saying it rose 25% tells you much more, because the size of the jump is measured against the starting price. Seventh graders use this for sales, tax, tips, population and scores.

Each line on this sheet reads like "From 60 to 75:" followed by two blanks. The first is for the percent, and the second is for the word increase or decrease. The page header gives the formula in words: new minus original, divided by the original, times 100. Students who have the formula in front of them can focus on the arithmetic instead of recalling the order.

Settings and what they do

  • Skill. The page opens on Percent of change (increase or decrease). Switch to Percent of a number for lines like 25% of 80, or What percent is it? for lines like "15 is what percent of 60?" The Mixed choice rotates through all three, which makes a good cumulative review.
  • Whole-number answers only. This toggle is on by default, so the percents come out cleanly, such as 20%, 50% or 75%. Turn it off for harder numbers, where students round each percent to the nearest tenth.
  • Number of problems. Anywhere from 6 to 24. Change problems print one per row, so 16 is a comfortable single page.

A sensible sequence is: percent of a number first (it is the multiplication part), then what percent, then change. Change problems combine subtraction, division and conversion to a percent in one go, so they are easier once each part is automatic.

Worked example: from 60 to 75

  1. Find the change by subtracting the original from the new amount: 75 − 60 = 15.
  2. Divide the change by the original amount, 60: 15 ÷ 60 = 0.25.
  3. Convert to a percent by multiplying by 100: 0.25 × 100 = 25%.
  4. The new amount is larger, so the word is increase.

Answer: a 25% increase.

Now a decrease: from 200 to 150. The change is 200 − 150 = 50. Divide by the original, 200: 50 ÷ 200 = 0.25, which is 25%. Since the amount went down, the answer is a 25% decrease. Notice that the number is positive both times. The word carries the direction, so a student should not write −25% on a sheet that has a separate blank for it.

An interesting follow-up for a stronger student: go from 75 back to 60. The change is still 15, but now it is 15 ÷ 75 = 0.2, a 20% decrease. A 25% rise and a 20% fall are the same dollar amount, because the starting point is different.

Mistakes the answer key will reveal

  • Dividing by the new amount. The student computes 15 ÷ 75 for the first example and gets 20%. The key says 25%, so the clue is a percent that is too small on increases and too large on decreases.
  • Missing the word. The percent is right but the second blank is empty. Treat the direction as part of the answer.
  • Forgetting the final ×100. An answer like 0.25 instead of 25% means the decimal was never converted.

Percents lean on proportional reasoning, so the ratios worksheet is a good warm-up. To strengthen the decimal conversions, try the decimals to fractions worksheet. Students who want more fraction-to-percent connections can also use the simplifying fractions worksheet.

Sources

  1. Common Core State Standards: Grade 7 Ratios and Proportional Relationships (7.RP.A.3, percent increase and decrease) thecorestandards.org