Consumer Math - Seventh Grade
Money, Prices, Discounts, Interest & Real-World Applications
1. Money Operations
Basic Operations with Money
Addition: Add money amounts (align decimal points)
Subtraction: Subtract money amounts (align decimal points)
Multiplication: Multiply money by a whole number or decimal
Division: Divide money amounts
Important Rules
• Always write money with 2 decimal places: $5.00, not $5
• Align decimal points when adding or subtracting
• Round to the nearest cent when necessary
• Use $ symbol in your final answer
2. Unit Prices
Definition
Unit price is the cost per ONE unit of an item
Used to compare prices and find the best deal
Unit Price Formula
Unit Price = Total Price ÷ Total Quantity
Example
Problem: A 12-pack of soda costs $6.00. What is the unit price per can?
Total Price = $6.00
Total Quantity = 12 cans
Unit Price = $6.00 ÷ 12 = $0.50 per can
Answer: $0.50 per can
Finding Total Price from Unit Price
Total Price = Unit Price × Quantity
Unit Prices with Unit Conversions
Example: A 32-ounce bottle costs $4.80. Find the price per pound.
Step 1: Convert ounces to pounds
32 oz ÷ 16 oz/lb = 2 lbs
Step 2: Calculate unit price
Unit Price = $4.80 ÷ 2 lbs = $2.40 per lb
Answer: $2.40 per pound
3. Tax, Discount, and More
Sales Tax
Sales Tax Amount = Original Price × Tax Rate
Total Cost = Original Price + Tax Amount
Or: Total Cost = Original Price × (1 + Tax Rate)
Discount
Discount Amount = Original Price × Discount Rate
Sale Price = Original Price − Discount Amount
Or: Sale Price = Original Price × (1 − Discount Rate)
Example: Tax
Problem: A shirt costs $25. Sales tax is 8%. What is the total cost?
Method 1:
Tax = $25 × 0.08 = $2.00
Total = $25 + $2.00 = $27.00
Method 2:
Total = $25 × 1.08 = $27.00
Answer: $27.00
Example: Discount
Problem: A $60 jacket is on sale for 30% off. What is the sale price?
Method 1:
Discount = $60 × 0.30 = $18
Sale Price = $60 − $18 = $42
Method 2:
Sale Price = $60 × 0.70 = $42
(100% − 30% = 70% = 0.70)
Answer: $42.00
4. Finding Original Price
Formula
Original Price = Sale Price ÷ (1 − Discount Rate)
Example
Problem: After a 25% discount, a watch costs $75. What was the original price?
Sale Price = $75
Discount = 25% = 0.25
Original Price = $75 ÷ (1 − 0.25)
Original Price = $75 ÷ 0.75
Original Price = $100
Answer: $100.00
5. Comparing Coupons
Types of Coupons
Dollar Off: $5 off, $10 off, etc.
Percent Off: 20% off, 30% off, etc.
How to Compare
Step 1: Calculate final price with each coupon
Step 2: Compare final prices
Step 3: Choose the coupon with the LOWEST final price
Example
Problem: A $80 item has two coupons: $15 off OR 25% off. Which is better?
Coupon A: $15 off
Final Price = $80 − $15 = $65
Coupon B: 25% off
Discount = $80 × 0.25 = $20
Final Price = $80 − $20 = $60
Better Coupon: 25% off (saves $20)
6. Estimating Tips
Tip Formula
Tip = Bill Amount × Tip Rate
Total = Bill + Tip
Common Tip Percentages
• 15% - Standard tip
• 18% - Good service
• 20% - Excellent service
Quick Tip Estimation
10% tip: Move decimal one place left
Example: $45.00 → 10% = $4.50
20% tip: Double the 10%
Example: 10% = $4.50, so 20% = $9.00
15% tip: Add 10% + half of 10%
Example: 10% = $4.50, half = $2.25, total = $6.75
7. Simple Interest
Definition
Simple interest is interest calculated only on
the ORIGINAL principal amount
Simple Interest Formula
I = PRT
or
I = (P × R × T)/100
Where:
I = Interest earned
P = Principal (original amount)
R = Rate (as decimal or percent/100)
T = Time (in years)
Total Amount Formula
A = P + I
or
A = P(1 + RT)
Example
Problem: You invest $1,000 at 5% annual interest for 3 years. Find the interest and total amount.
P = $1,000, R = 5% = 0.05, T = 3 years
Calculate Interest:
I = PRT = 1000 × 0.05 × 3
I = $150
Calculate Total Amount:
A = P + I = $1,000 + $150 = $1,150
Interest: $150, Total Amount: $1,150
8. Compound Interest
Definition
Compound interest is interest calculated on
the PRINCIPAL plus previously earned interest
Interest earns interest!
Compound Interest Formula
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (starting amount)
r = Annual interest rate (as decimal)
n = Number of times compounded per year
t = Time in years
Compounding Frequency
• Annually: n = 1 (once per year)
• Semi-annually: n = 2 (twice per year)
• Quarterly: n = 4 (four times per year)
• Monthly: n = 12 (twelve times per year)
Example: Annual Compounding
Problem: $1,000 invested at 5% interest compounded annually for 3 years.
P = $1,000, r = 0.05, n = 1, t = 3
A = 1000(1 + 0.05/1)^(1×3)
A = 1000(1.05)³
A = 1000(1.157625)
A = $1,157.63
Interest = A − P = $1,157.63 − $1,000 = $157.63
Total Amount: $1,157.63 (Interest: $157.63)
9. Multi-Step Problems with Percents
Strategy
Step 1: Read carefully and identify what you need to find
Step 2: Solve one step at a time
Step 3: Use each result for the next step
Step 4: Check your final answer
Example
Problem: A $80 item is on sale for 25% off. Then you have a coupon for an additional 10% off the sale price. Tax is 8%. What is the final price?
Step 1: Apply first discount (25% off)
Discount = $80 × 0.25 = $20
Price after 1st discount = $80 − $20 = $60
Step 2: Apply coupon (10% off sale price)
Discount = $60 × 0.10 = $6
Price after coupon = $60 − $6 = $54
Step 3: Add tax (8%)
Tax = $54 × 0.08 = $4.32
Final Price = $54 + $4.32 = $58.32
Final Price: $58.32
Quick Reference: Consumer Math Formulas
| Concept | Formula |
|---|---|
| Unit Price | Total Price ÷ Quantity |
| Sales Tax | Price × Tax Rate |
| Discount Amount | Price × Discount Rate |
| Sale Price | Original × (1 − Discount Rate) |
| Tip | Bill × Tip Rate |
| Simple Interest | I = PRT |
| Compound Interest | A = P(1 + r/n)^(nt) |
💡 Important Tips to Remember
✓ Always include $ symbol in money answers
✓ Round to 2 decimal places for money (cents)
✓ Unit price: Lower unit price = better deal
✓ Sales tax increases price - add to original
✓ Discounts decrease price - subtract from original
✓ Compare final prices when choosing coupons
✓ Tips are calculated on the bill BEFORE tax
✓ Simple interest: calculated only on principal
✓ Compound interest: earns more than simple interest
✓ Multi-step problems: solve one step at a time
🧠 Memory Tricks & Strategies
Unit Price:
"Price per unit? Divide price by the amount - that's the trick, don't doubt!"
Tax and Discount:
"Tax adds up, discount brings down - remember this in every town!"
Simple Interest:
"PRT is the key - Principal, Rate, Time make money grow free!"
Compound Interest:
"Interest on interest, that's the deal - compound makes your money more real!"
Comparing Coupons:
"Calculate both, compare with care - choose the one that saves you more to spare!"
Tips:
"10% is easy - move decimal left! 20% is double, that's the best!"
Master Consumer Math! 💰 📊
Remember: These skills help you make smart money decisions every day!