Instructions
Welcome, Detective! Your mission is to become an expert at converting numbers. Stores use fractions, decimals, and percentages to advertise sales, and it's your job to crack the code and find the best deals. Follow the steps below to complete your training.
- Read the Helpful Hints box for a quick reminder on how to convert between the three forms.
- Complete Part 1 by filling in the empty cells in the Conversion Grid.
- In Part 2, use your conversion skills to compare discounts and identify the best value.
- Apply all your knowledge in Part 3 to solve a real-world shopping problem.
- For an extra challenge, try the optional Brain Booster question.
Helpful Hints: Your Detective's Toolkit
- Fraction to Decimal: Divide the top number (numerator) by the bottom number (denominator). Example: 1/4 = 1 ÷ 4 = 0.25
- Decimal to Percent: Move the decimal point two places to the right and add a % sign. Example: 0.25 → 25.%
- Percent to Decimal: Move the decimal point two places to the left and remove the % sign. Example: 75% → .75 → 0.75
- Decimal to Fraction: Write the decimal as a fraction over 10, 100, or 1000 based on the number of decimal places, then simplify. Example: 0.8 = 8/10 = 4/5
Part 1: The Conversion Grid
Complete the table below by converting the given number into its other two forms. The first row is done for you as an example.
| Fraction (Simplified) | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 3/4 | ||
| 0.2 | ||
| 80% | ||
| 1/5 | ||
| 1.25 |
Part 2: The Shopping Spree Showdown
For each pair of items, circle or write down which option offers the bigger discount. Show your work!
-
A new video game is on sale. Which is the better deal?
- Store A: 1/4 off the original price.
- Store B: 20% off the original price.
Work Space:
Answer:
-
You want to buy a pair of headphones that originally cost $50. Which store has the lower price?
- Store X: A discount of 0.3 off the price.
- Store Y: A 25% off sale.
Work Space:
Answer:
Part 3: Real-World Detective Work
A new bicycle costs $300. Three different stores have a sale on it. Your mission is to figure out which store offers the best final price.
- Cycle Central: Offers a 1/3 off coupon.
- Bike Bonanza: Has a 30% off store-wide sale.
- Two-Wheel Town: Advertises a discount of 0.35 off the original price.
Calculate the final price at each store to find the best deal.
-
Cycle Central Final Price:
Calculation:
-
Bike Bonanza Final Price:
Calculation:
-
Two-Wheel Town Final Price:
Calculation:
Conclusion: The best deal is at ____.
Brain Booster Challenge (Optional)
A jacket is on sale for 20% off its original price of $80. You also have a coupon for an additional 10% off the sale price. What is the final price you will pay? Is this the same as a single 30% discount?
Answer Key
Part 1: The Conversion Grid
| Fraction (Simplified) | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 4/5 | 0.8 | 80% |
| 1/5 | 0.2 | 20% |
| 1 1/4 or 5/4 | 1.25 | 125% |
Part 2: The Shopping Spree Showdown
- Store A is the better deal. (1/4 = 25%. Since 25% > 20%, 1/4 off is a bigger discount).
- Store Y has the lower price. (Store X discount is 0.3 = 30%. $50 0.3 = $15 off; Final Price = $35. Store Y discount is 25%. $50 0.25 = $12.50 off; Final Price = $37.50. Wait, check the math. Store X discount is $15 off, making the price $35. Store Y discount is 25% off, which is $12.50 off, making the price $37.50. So Store X has the lower price. Correction: The question asks for the lower price, not the bigger discount. 0.3 = 30% off. 30% of $50 is $15. Price is $35. 25% of $50 is $12.50. Price is $37.50. Store X has the lower price.)
Part 3: Real-World Detective Work
- Cycle Central Final Price: $200 (1/3 of $300 is $100 off. $300 - $100 = $200).
- Bike Bonanza Final Price: $210 (30% of $300 is $90 off. $300 - $90 = $210).
- Two-Wheel Town Final Price: $195 (0.35 of $300 is $105 off. $300 - $105 = $195).
- Conclusion: The best deal is at Two-Wheel Town.
Brain Booster Challenge
- First discount: 20% of $80 is $16. The sale price is $80 - $16 = $64.
- Second discount: 10% of the sale price ($64) is $6.40.
- Final price: $64 - $6.40 = $57.60.
- This is not the same as a 30% discount. A 30% discount off $80 would be $24 off, for a final price of $56. Taking two smaller percentages off in sequence results in a smaller total discount.