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Grade 7 · lesson 2 of 4

Identify the Base of Percent Increase

Percent change compares the change amount with the original amount.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: A fictional club changes from 200 to 220 members. What is the percent increase? Candidate answers: (A) 0.1 % (B) 10 % (C) 110 % (D) 9.0909 %.
  • Independent check inputs: A fictional club changes from 300 to 360 members. What is the percent increase? Candidate answers: (A) 0.2 % (B) 120 % (C) 16.6667 % (D) 20 %.

Learn the idea

A percent is a ratio per hundred, but its base quantity matters. Successive percent operations act on successive amounts; reverse problems recover the original base rather than simply adding back a percentage. Percent change compares the change amount with the original amount. The new total includes both the original and the change, so it has a different percent interpretation.

Here is the method on the supplied teaching case. The change magnitude is 20. Divide by original 200: 20/200=0.1. Multiply by 100 to get 10% increase. The denominator remains the original amount.

The denominator is the original amount, not the new amount. Report an increase rate separately from the new total expressed as a percent of the original; they answer different questions.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: A fictional club changes from 200 to 220 members. What is the percent increase? Candidate answers: (A) 0.1 % (B) 10 % (C) 110 % (D) 9.0909 %. Solution: The change magnitude is 20. Divide by original 200: 20/200=0.1. Multiply by 100 to get 10% increase. The denominator remains the original amount. The final answer is 10 %. The denominator is the original amount, not the new amount. Report an increase rate separately from the new total expressed as a percent of the original; they answer different questions.

Your turn

Check your reasoning

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Helpful tips
  • Percent change compares the change amount with the original amount.
  • The denominator is the original amount, not the new amount.
A fictional club changes from 300 to 360 members. What is the percent increase?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

20 %

The change magnitude is 60. Divide by original 300: 60/300=0.2. Multiply by 100 to get 20% increase. The denominator remains the original amount.

Take it further

Changed-input task: A fictional club changes from 900 to 1170 members. What is the percent increase? Candidate answers: (A) 0.3 % (B) 130 % (C) 23.0769 % (D) 30 %. Show the mathematical reason, not only the selected answer. Expected result: 30 %. The change magnitude is 270. Divide by original 900: 270/900=0.3. Multiply by 100 to get 30% increase. The denominator remains the original amount.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. A fictional club changes from 400 to 500 members. What is the percent increase?
Need a hint?
  • Percent change compares the change amount with the original amount.
  • The denominator is the original amount, not the new amount.
2. A fictional club changes from 500 to 300 members. What is the percent decrease?
Need a hint?
  • Percent change compares the change amount with the original amount.
  • The denominator is the original amount, not the new amount.
3. A fictional club changes from 600 to 900 members. What is the percent increase?
Need a hint?
  • Percent change compares the change amount with the original amount.
  • The denominator is the original amount, not the new amount.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

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