Level 2 · Enrichment

Reveal Math · Unit 4 · Supplemental

Decimals & Percents

Grade 6 · Standards 6.NS.B.2–3, 6.RP.A.3c — multi-step decimal & percent applications

Name: Date:

Challenge Problems

Directions: Solve and show your strategy. For each "Explain" prompt, justify your reasoning in a complete sentence.
  1. A $48 jacket is 25% off, then 8% sales tax is added to the sale price. What is the final price? Multi-step
    Explain: why can't you just subtract 25% − 8%?
  2. A $65 dinner bill gets an 18% tip added. What is the total bill? Real-world
  3. Order from least to greatest: 0.6, 3/5, 65%, 0.58. Reasoning
    Explain how converting to one common form makes ordering easier.
  4. A store marks up a $40 item by 30%, then later takes 30% off the new price. Is the final price back to $40? Reasoning
    Explain why or why not.
  5. 15 of 25 students passed a quiz. What percent passed? What percent did not? Multi-step
  6. Compute 7.2 × 0.05 and explain how to place the decimal point without a calculator. Reasoning
  7. A recipe needs 0.75 L of milk per batch. You have 5 L. How many full batches can you make, and how much milk is left over? Multi-step
  8. Write a fraction, a decimal, and a percent that are all equal and all different from one-half. Then prove they are equal. Open-ended
  9. A number increased by 20% is 96. What was the original number? Reasoning
    Explain why you divide rather than just take 20% of 96.
  10. Two stores sell the same $60 game: Store A takes 20% off; Store B takes $10 off then 10% off. Which is cheaper? Real-world

Stretch Investigation

Real-world application: Plan a $100 shopping trip. Pick at least four items with real prices. Apply a 15% off coupon to the most expensive item only, then add 6% sales tax to your whole order. Show every calculation, find the final total, and report how much you have left of your $100 budget. Then explain whether applying the coupon to a different item would have saved more.

Answer Key

  1. Sale price 48 × 0.75 = $36; tax 36 × 1.08 = $38.88. Percents apply to different amounts, so they can't be combined directly.
  2. Tip 65 × 0.18 = $11.70; total 65 + 11.70 = $76.70.
  3. Convert: 0.58, 0.6, 3/5 = 0.6, 65% = 0.65 → order 0.58, 0.6 = 3/5, 65%.
  4. Marked up: 40 × 1.30 = $52; then 52 × 0.70 = $36.40. No — it ends below $40 because 30% off is taken on the larger price.
  5. 15 ÷ 25 = 0.60 = 60% passed; 40% did not.
  6. 72 × 5 = 360 → two extra decimal places (one + two) → 0.360 = 0.36.
  7. 5 ÷ 0.75 = 6.67 → 6 full batches use 4.5 L; 0.5 L left over.
  8. Answers vary, e.g., 3/4 = 0.75 = 75% (3 ÷ 4 = 0.75; ×100 = 75%).
  9. Original × 1.20 = 96 → 96 ÷ 1.20 = 80. The 96 already includes the increase, so you undo it by dividing.
  10. A: 60 × 0.80 = $48. B: (60 − 10) × 0.90 = $45. Store B is cheaper.
  11. Stretch: answers vary; full credit needs correct coupon, tax math, a final total, and a justified comparison.