The Life Starter
Sign up
Grade 9 · lesson 2 of 4

Retain a Fraction of the Current Amount

A fixed percent decrease preserves the same fraction each period.

About 20 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: A fictional model loses 20% each period from 200. What remains after two periods? Candidate answers: (A) 127 (B) 128 (C) 129 (D) 256.
  • Independent check inputs: A fictional model loses 20% each period from 300. What remains after two periods? Candidate answers: (A) 191 (B) 192 (C) 193 (D) 384.

Learn the idea

An exponential pattern changes by a constant multiplicative ratio over equal input steps. This differs from a linear pattern’s constant addition and can model supplied growth, decay or ordered geometric sequence terms. A fixed percent decrease preserves the same fraction each period. The retained fraction multiplies the current amount, so absolute losses get smaller as the remaining amount shrinks.

Here is the method on the supplied teaching case. Each period retains 80%, so multiply by 0.8 twice: 200×0.8²=128. The second loss is based on the smaller current amount.

Losing twenty percent twice does not mean losing forty percent of the original. Track the surviving multiplier at each period, keeping sufficient digits until the final requested rounding.

  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 model loses 20% each period from 200. What remains after two periods? Candidate answers: (A) 127 (B) 128 (C) 129 (D) 256. Solution: Each period retains 80%, so multiply by 0.8 twice: 200×0.8²=128. The second loss is based on the smaller current amount. The final answer is 128. Losing twenty percent twice does not mean losing forty percent of the original. Track the surviving multiplier at each period, keeping sufficient digits until the final requested rounding.

Your turn

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Helpful tips
  • A fixed percent decrease preserves the same fraction each period.
  • Losing twenty percent twice does not mean losing forty percent of the original.
A fictional model loses 20% each period from 300. What remains after two periods?

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

See the answer and explanation

192

Each period retains 80%, so multiply by 0.8 twice: 300×0.8²=192. The second loss is based on the smaller current amount.

Take it further

Changed-input task: A fictional model loses 20% each period from 900. What remains after two periods? Candidate answers: (A) 1152 (B) 575 (C) 576 (D) 577. Show the mathematical reason, not only the selected answer. Expected result: 576. Each period retains 80%, so multiply by 0.8 twice: 900×0.8²=576. The second loss is based on the smaller current amount.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.

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 model loses 20% each period from 400. What remains after two periods?
Need a hint?
  • A fixed percent decrease preserves the same fraction each period.
  • Losing twenty percent twice does not mean losing forty percent of the original.
2. A fictional model loses 20% each period from 500. What remains after two periods?
Need a hint?
  • A fixed percent decrease preserves the same fraction each period.
  • Losing twenty percent twice does not mean losing forty percent of the original.
3. A fictional model loses 20% each period from 600. What remains after two periods?
Need a hint?
  • A fixed percent decrease preserves the same fraction each period.
  • Losing twenty percent twice does not mean losing forty percent of the original.

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.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.