💰 Money and Time - Complete Notes & Formulas 🕐
1. Add and Subtract Money Amounts
Addition Formula:
$A.BC + $D.EF = $Total
Example: $12.45 + $7.89
$12.45
+ $7.89
————————
$20.34
Subtraction Formula:
$A.BC − $D.EF = $Difference
Example: $25.50 − $8.75
$25.50
− $8.75
————————
$16.75
- Always write dollar amounts with two decimal places (e.g., $5.00 not $5)
- Line up the decimal points vertically
- Add zeros if needed: $8 = $8.00
- Remember to include the dollar sign ($) in your answer
2. Add and Subtract Money: Word Problems
Key Keywords:
| Addition Keywords | Subtraction Keywords |
|---|---|
| Total, Sum, Altogether, Combined, In all, Both | Difference, Left, Remaining, Change, How much more, Less than |
Addition Example:
Sarah bought a book for $12.75 and a pen for $3.50. How much did she spend in total?
Solution:
1 Identify: We need to find the total
2 Operation: Addition (total means add)
3 Calculate: $12.75 + $3.50 = $16.25
Subtraction Example:
Mike had $50.00. He bought a toy for $18.25. How much money does he have left?
Solution:
1 Identify: We need to find what's left
2 Operation: Subtraction (left means subtract)
3 Calculate: $50.00 − $18.25 = $31.75
3. Add and Subtract Money: Multi-Step Word Problems
Example:
Emma had $75.00. She bought a shirt for $22.50 and a hat for $15.75. Then she earned $20.00 doing chores. How much money does Emma have now?
Solution:
1 Calculate total spent:
$22.50 + $15.75 = $38.25
2 Subtract from original amount:
$75.00 − $38.25 = $36.75
3 Add money earned:
$36.75 + $20.00 = $56.75
- Read the problem carefully and identify all the steps
- Decide which operation to use for each step
- Solve one step at a time
- Use your answer from one step in the next step
- Check if your final answer makes sense
4. Multiply Money Amounts
Steps to Multiply Money:
1 Ignore the dollar sign and decimal point temporarily
2 Multiply the numbers as whole numbers
3 Count total decimal places in the original amount (usually 2)
4 Place the decimal point in your answer
5 Add the dollar sign
Example 1: $3.50 × 4
1 Think: 350 × 4 = 1400
2 Place decimal (2 places from right): 14.00
3 Add dollar sign: $14.00
Example 2: $12.75 × 6
1 Think: 1275 × 6 = 7650
2 Place decimal: 76.50
3 Answer: $76.50
5. Multiply Money Amounts: Word Problems
Multiplication Keywords:
Example 1:
One notebook costs $4.25. How much do 5 notebooks cost?
Solution:
1 Identify: Cost per item × number of items
2 Calculate: $4.25 × 5 = $21.25
Example 2:
A movie ticket costs $8.75. If 3 friends go to the movie, how much will they pay in total?
Solution:
$8.75 × 3 = $26.25
6. Multiply Money Amounts: Multi-Step Word Problems
Example:
A bakery sells cupcakes for $3.50 each and cookies for $2.25 each. Lisa buys 4 cupcakes and 6 cookies. How much does she spend in total?
Solution:
1 Calculate cost of cupcakes:
$3.50 × 4 = $14.00
2 Calculate cost of cookies:
$2.25 × 6 = $13.50
3 Add both amounts:
$14.00 + $13.50 = $27.50
Total = (Price₁ × Quantity₁) + (Price₂ × Quantity₂) + ...
7. Divide Money Amounts
Steps to Divide Money:
1 Set up the division problem
2 Place the decimal point in the answer directly above the decimal in the dividend
3 Divide as usual
4 Add the dollar sign to your answer
Example 1: $24.00 ÷ 4
$6.00
————————
4 ) $24.00
24
————
0
Answer: $6.00
Example 2: $36.75 ÷ 3
Solution: Divide 3675 ÷ 3 = 1225
Place decimal: 12.25
Answer: $12.25
8. Divide Money Amounts: Word Problems
Division Keywords:
Example 1:
Four friends share a pizza bill of $28.00 equally. How much does each friend pay?
Solution:
1 Identify: Total ÷ number of people
2 Calculate: $28.00 ÷ 4 = $7.00
Example 2:
A pack of 5 pens costs $12.50. What is the cost of one pen?
Solution:
$12.50 ÷ 5 = $2.50
9. Price Lists
How to Work with Price Lists:
1 Read the price list carefully
2 Identify all items needed
3 Find the price for each item
4 Multiply if buying more than one of the same item
5 Add all costs together for the total
Example Price List:
| Item | Price |
|---|---|
| Pencil | $0.75 |
| Eraser | $1.25 |
| Notebook | $3.50 |
| Ruler | $2.00 |
Problem: Buy 2 pencils, 1 notebook, and 1 ruler. What's the total cost?
Solution:
Pencils: $0.75 × 2 = $1.50
Notebook: $3.50 × 1 = $3.50
Ruler: $2.00 × 1 = $2.00
Total: $1.50 + $3.50 + $2.00 = $7.00
10. Unit Prices
Unit Price = Total Price ÷ Number of Units
What is Unit Price?
The unit price is the cost of ONE item or ONE unit (like price per pound, per ounce, per item).
Example 1:
A pack of 8 juice boxes costs $6.40. What is the unit price (cost per juice box)?
Solution:
Unit Price = $6.40 ÷ 8 = $0.80 per juice box
Example 2 - Comparing Unit Prices:
Brand A: 3 apples for $2.25
Brand B: 5 apples for $3.50
Which is the better buy?
Solution:
Brand A unit price: $2.25 ÷ 3 = $0.75 per apple
Brand B unit price: $3.50 ÷ 5 = $0.70 per apple
Answer: Brand B is the better buy! (Lower unit price)
11. Find the Number of Each Type of Coin
US Coin Values:
| Coin | Value | Symbol |
|---|---|---|
| Penny | 1 cent | $0.01 or 1¢ |
| Nickel | 5 cents | $0.05 or 5¢ |
| Dime | 10 cents | $0.10 or 10¢ |
| Quarter | 25 cents | $0.25 or 25¢ |
| Half Dollar | 50 cents | $0.50 or 50¢ |
| Dollar Coin | 100 cents | $1.00 |
Total Value = (# of Pennies × $0.01) + (# of Nickels × $0.05) + (# of Dimes × $0.10) + (# of Quarters × $0.25)
Example 1:
You have 3 quarters, 2 dimes, and 4 pennies. How much money do you have?
Solution:
Quarters: 3 × $0.25 = $0.75
Dimes: 2 × $0.10 = $0.20
Pennies: 4 × $0.01 = $0.04
Total: $0.75 + $0.20 + $0.04 = $0.99
Example 2 - Finding Number of Coins:
Sarah has $1.85 in quarters and dimes. She has 5 quarters. How many dimes does she have?
Solution:
1 Value of quarters: 5 × $0.25 = $1.25
2 Remaining amount: $1.85 − $1.25 = $0.60
3 Number of dimes: $0.60 ÷ $0.10 = 6 dimes
- 1 nickel = 5 pennies
- 1 dime = 2 nickels = 10 pennies
- 1 quarter = 5 nickels = 2 dimes + 1 nickel = 25 pennies
- 1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
12. Convert Time Units
Time Conversion Chart:
| Conversion | Formula |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 hour | 3,600 seconds (60 × 60) |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 365 days (366 in leap year) |
| 1 year | 52 weeks |
| 1 year | 12 months |
Larger → Smaller: MULTIPLY
Smaller → Larger: DIVIDE
Converting Larger to Smaller Units (Multiply):
Example 1: Convert 5 hours to minutes
Solution:
1 Identify: Hours → Minutes (larger to smaller)
2 Formula: Hours × 60 = Minutes
3 Calculate: 5 × 60 = 300 minutes
Example 2: Convert 3 weeks to days
Solution:
3 weeks × 7 days/week = 21 days
Converting Smaller to Larger Units (Divide):
Example 3: Convert 180 seconds to minutes
Solution:
1 Identify: Seconds → Minutes (smaller to larger)
2 Formula: Seconds ÷ 60 = Minutes
3 Calculate: 180 ÷ 60 = 3 minutes
Example 4: Convert 144 hours to days
Solution:
144 hours ÷ 24 hours/day = 6 days
Multi-Step Time Conversions:
Example 5: Convert 2 hours to seconds
Solution:
1 First convert hours to minutes: 2 × 60 = 120 minutes
2 Then convert minutes to seconds: 120 × 60 = 7,200 seconds
OR use direct conversion: 2 hours × 3,600 seconds/hour = 7,200 seconds
- Remember: 60 is the magic number for seconds/minutes and minutes/hours
- Going DOWN the chart (hours→minutes→seconds) = MULTIPLY
- Going UP the chart (seconds→minutes→hours) = DIVIDE
- For multi-step conversions, convert one step at a time
- Always label your units to avoid confusion
- 2 minutes = 120 seconds
- 5 minutes = 300 seconds
- 30 minutes = 0.5 hours
- 90 minutes = 1.5 hours
- 48 hours = 2 days
- 72 hours = 3 days
- 14 days = 2 weeks
📚 Quick Reference Summary
Money Operations:
- Addition & Subtraction: Line up decimal points, always use 2 decimal places
- Multiplication: Price × Quantity = Total Cost
- Division: Total ÷ Number = Per Item Cost (Unit Price)
- Unit Price: Total Price ÷ Number of Units (Lower = Better Deal)
Coin Values (memorize these!):
- Penny = 1¢ | Nickel = 5¢ | Dime = 10¢ | Quarter = 25¢ | Dollar = 100¢
Time Conversions (memorize these!):
- 1 minute = 60 seconds
- 1 hour = 60 minutes = 3,600 seconds
- 1 day = 24 hours
- 1 week = 7 days
- 1 year = 365 days = 52 weeks = 12 months
🌟 Practice makes perfect! Keep reviewing these formulas and solving problems! 🌟