I'll solve each problem step by step, carefully checking my calculations.
Problem 1: Discounts
- Original price: $15.99
- Discount: 20%
- Calculate discount amount: $15.99 × 0.20 = $3.198
- Subtract discount: $15.99 - $3.198 = $12.792
- Round to nearest cent: $12.79
Let me verify: $15.99 × 0.80 (which is 100% - 20%) = $12.792 ≈ $12.79 ✓
Problem 2: Equations
- Start with 0.5
- Multiply by 0.3: 0.5 × 0.3 = 0.15
- Add 0.2: 0.15 + 0.2 = 0.35
Final answer: 0.35 ✓
Problem 3: Sales
- Price per sticker: $0.99
- Number of stickers: 7
- Total cost: $0.99 × 7 = $6.93
Check: $1 × 7 = $7, minus $0.01 × 7 = $0.07, so $7 - $0.07 = $6.93 ✓
Problem 4: Emoji Pizza Slices
- Total slices: 8
- Mia eats: 3.75 slices
- Remaining: 8 - 3.75 = 4.25 slices
Check: 3.75 + 4.25 = 8 ✓
Problem 5: Ratios
- Total students: 40
- Smiley face emoji: 2/5 of 40 = (2/5) × 40 = 16 students
- Heart emoji: 1/4 of 40 = (1/4) × 40 = 10 students
- Thumbs-up emoji: rest of the class
- Thumbs-up = 40 - 16 - 10 = 14 students
Check: 16 + 10 + 14 = 40 ✓
Problem 6: Lengths
- Total characters: 140
- Emojis: 3/10 of 140 = (3/10) × 140 = 42 emojis
- Non-emoji characters: 140 - 42 = 98 characters
Check: 42 + 98 = 140 ✓
Problem 7: Discounts Part II
- Original price: $4.50
- Discount: 30%
- Calculate discount amount: $4.50 × 0.30 = $1.35
- Subtract discount: $4.50 - $1.35 = $3.15
Alternative check: $4.50 × 0.70 = $3.15 ✓
Problem 8: Conversions
- Given: 2.5 kilograms = 2500 grams
- To find conversion factor from kg to g
- Divide both sides by 2.5: 1 kilogram = 2500 ÷ 2.5 grams
- 2500 ÷ 2.5 = 1000
- So 1 kilogram = 1000 grams
The conversion factor is 1000 (multiply kilograms by 1000 to get grams) ✓
Problem 9: Party
- Total guests: 48
- Wear emoji costumes: 3/8 of 48
- Calculate: (3/8) × 48 = 3 × 6 = 18 guests wear emoji costumes
- Wear other costumes: 48 - 18 = 30 guests
Check: 18 + 30 = 48 ✓
Problem 10: Repeating Decimals
- Convert 1/3 to decimal
- 1 ÷ 3 = 0.333... (the 3 repeats forever)
- Written as 0.3 or 0.3̅
The decimal representation is 0.333... or 0.̅3 ✓
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Final Answer:
1. $12.79
2. 0.35
3. $6.93
4. 4.25 slices
5. 14 students
6. 98 characters
7. $3.15
8. 1000
9. 30 guests
10. 0.333... (or 0.3)
Parent Tip: Review the logic above to help your child master the concept of multiplying and dividing decimals word problem worksheet.
