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Grade 7 · unit review

Review: Percent Changes, Reverse Percents, and Simple Interest

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.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. A fictional item costs $140. Apply a 20% discount, then 5% tax to the discounted price. What is the final total?
Need a hint?
  • A discount removes a percent of the original price.
  • Use the taxable base stated in the fictional problem; actual tax rules may differ.
2. A fictional club changes from 700 to 735 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.
3. After a 25% reduction, a fictional fee is $105. What was the original fee?
Need a hint?
  • A reduced amount is the surviving percent of an unknown original.
  • Adding the discount rate to the reduced amount uses the wrong base.
4. A fictional simple-interest model uses principal $700, annual rate 4%, and 8 years. What interest alone accrues?
Need a hint?
  • Simple interest is proportional to principal, time, and rate.
  • Convert the annual percent to a decimal and use years for time.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. A fictional item costs $180. Apply a 20% discount, then 5% tax to the discounted price. What is the final total? Candidate answers: (A) 135 USD (B) 151.2 USD (C) 153 USD (D) 189 USD. 2. 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 %. 3. After a 25% reduction, a fictional fee is $135. What was the original fee? Candidate answers: (A) 101.25 USD (B) 160 USD (C) 168.75 USD (D) 180 USD. 4. A fictional simple-interest model uses principal $900, annual rate 4%, and 10 years. What interest alone accrues? Candidate answers: (A) 1260 USD (B) 36 USD (C) 360 USD (D) 432.2199 USD.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 151.2 USD. Keep 80% after the discount: $180×0.80=$144.00. Then multiply by 1.05 for tax: $151.20. Tax is not applied to the original price. 2. 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. 3. 180 USD. The remaining fee is 75% of the original. Solve 0.75p=135 by dividing by 0.75: p=180. Adding 25% of the reduced fee would use the wrong base. 4. 360 USD. Use I=Prt=900×0.04×10=360.0. Simple interest uses the original principal every year. This question asks for interest, not principal plus interest.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.