Money and Time - Fifth Grade Math
Complete Notes & Formulas
1. Add and Subtract Money Amounts
Money Notation
Money is written with a dollar sign ($) and two decimal places for cents.
Format: $XX.XX
Example: $25.50 (Twenty-five dollars and fifty cents)
Rules for Adding Money
Step 1: Write the amounts in columns
Step 2: Line up the decimal points (VERY IMPORTANT!)
Step 3: Add the cents first (hundredths place)
Step 4: Add the dimes (tenths place)
Step 5: Add the dollars
Step 6: Write the $ sign in the answer
Rules for Subtracting Money
Step 1: Write the larger amount first
Step 2: Line up the decimal points
Step 3: Subtract from right to left (cents, then dollars)
Step 4: Borrow from the next place value if needed
Step 5: Write the $ sign in the answer
Examples
Addition Example: $45.75 + $23.50
$45.75 + $23.50 -------- $69.25
Subtraction Example: $82.40 - $37.65
$82.40 - $37.65 -------- $44.75
Important Reminder
Always keep two decimal places in your answer. If the answer is $45.5, write it as $45.50
2. Add and Subtract Money: Word Problems
Key Words for Money Operations
Operation | Key Words |
---|---|
Addition | Total, altogether, combined, spent in all, sum |
Subtraction | Change, left over, remaining, difference, how much more |
Steps to Solve
Step 1: Read the problem carefully
Step 2: Identify the money amounts
Step 3: Decide: Add or Subtract?
Step 4: Write the equation
Step 5: Solve and check if the answer makes sense
Examples
"Emma bought a book for $12.75 and a pen for $3.25. How much did she spend in total?"
Identify: Two amounts to add
Equation: $12.75 + $3.25 = ?
Solution: $12.75 + $3.25 = $16.00
Answer: Emma spent $16.00
"Jack had $50.00. He bought a toy for $28.75. How much money does he have left?"
Identify: Money left = subtract
Equation: $50.00 - $28.75 = ?
Solution: $50.00 - $28.75 = $21.25
Answer: Jack has $21.25 left
3. Add and Subtract Money: Multi-Step Word Problems
What are Multi-Step Problems?
Problems that require more than one operation (add and subtract) to find the answer.
Strategy
• Break the problem into smaller steps
• Solve one step at a time
• Use each answer in the next step
Example
"Sophia went to the mall with $100.00. She bought a shirt for $24.50, shoes for $45.75, and a hat for $12.00. How much money does she have left?"
Step 1: Find total spent
$24.50 + $45.75 + $12.00 = $82.25
Step 2: Subtract from original amount
$100.00 - $82.25 = $17.75
Answer: Sophia has $17.75 left
4. Multiply Money Amounts
When Do We Multiply Money?
When buying multiple items of the same price, or finding total cost for repeated purchases.
Formula
Total Cost = Price per Item × Number of Items
Steps to Multiply Money
Step 1: Ignore the $ and decimal point temporarily
Step 2: Multiply the numbers
Step 3: Count decimal places in the money amount (always 2)
Step 4: Place decimal point 2 places from the right in the answer
Step 5: Add the $ sign
Examples
Example 1: $7.25 × 4
• Ignore decimal: 725 × 4 = 2900
• Place decimal 2 places from right: 29.00
• Answer: $29.00
Example 2: $15.50 × 6
• 1550 × 6 = 9300
• Place decimal: 93.00
• Answer: $93.00
5. Multiply Money Amounts: Word Problems
Key Words for Multiplication
• Each (price per item)
• Per (cost per unit)
• Times (multiple purchases)
• Total cost for (multiple items)
Example
"A movie ticket costs $8.75. If Alex buys 5 tickets for his family, how much does he pay in total?"
Given: Price per ticket = $8.75, Number = 5
Equation: $8.75 × 5 = ?
Solve: $8.75 × 5 = $43.75
Answer: Alex pays $43.75 in total
6. Multiply Money Amounts: Multi-Step Word Problems
Example
"A bakery sells cupcakes for $2.50 each and cookies for $1.75 each. If Maria buys 6 cupcakes and 8 cookies, how much does she spend in total?"
Step 1: Find cost of cupcakes
$2.50 × 6 = $15.00
Step 2: Find cost of cookies
$1.75 × 8 = $14.00
Step 3: Add both amounts
$15.00 + $14.00 = $29.00
Answer: Maria spends $29.00 in total
7. Divide Money Amounts
When Do We Divide Money?
• Finding price per item
• Splitting costs equally
• Finding how many items can be bought
Formula
Price per Item = Total Cost ÷ Number of Items
Each Person Pays = Total Cost ÷ Number of People
Steps to Divide Money
Step 1: Set up the division problem
Step 2: Keep the decimal point in the quotient above the dividend's decimal
Step 3: Divide as usual
Step 4: Add zeros after the decimal if needed
Step 5: Add the $ sign to the answer
Examples
Example 1: $36.00 ÷ 4
• 36 ÷ 4 = 9
• Keep decimal: 9.00
• Answer: $9.00
Example 2: $45.50 ÷ 7
• 455 ÷ 7 = 65
• Place decimal: 6.50
• Answer: $6.50
8. Divide Money Amounts: Word Problems
Key Words for Division
• Each person pays
• Shared equally
• Split evenly
• Divided among
• Price per item
Example
"Four friends split the cost of a $52.00 pizza equally. How much does each person pay?"
Given: Total = $52.00, People = 4
Equation: $52.00 ÷ 4 = ?
Solve: $52.00 ÷ 4 = $13.00
Answer: Each person pays $13.00
9. Price Lists
What is a Price List?
A price list is a table showing items and their prices. You use it to find costs and calculate totals.
How to Use a Price List
Step 1: Find the item on the list
Step 2: Look at its price
Step 3: If buying multiple items, multiply price × quantity
Step 4: Add all item costs for the total
Example Price List
Item | Price |
---|---|
Apple | $0.75 |
Orange | $1.25 |
Banana (bunch) | $2.50 |
Milk (gallon) | $4.25 |
Problem: Find the cost of 3 apples and 2 oranges.
Apples: $0.75 × 3 = $2.25
Oranges: $1.25 × 2 = $2.50
Total: $2.25 + $2.50 = $4.75
10. Unit Prices
What is a Unit Price?
A unit price is the cost of one single item or one unit of measurement (per pound, per gallon, per item, etc.)
Unit Price Formula
Unit Price = Total Cost ÷ Number of Units
Why is Unit Price Important?
• Helps compare prices of different package sizes
• Shows which is the better deal
• Used in grocery shopping
Steps to Find Unit Price
Step 1: Identify the total cost
Step 2: Identify the number of units
Step 3: Divide: Total Cost ÷ Number of Units
Step 4: Write answer with "per" (per pound, per item, etc.)
Examples
Example 1: A pack of 8 pencils costs $4.00. What is the unit price per pencil?
Formula: Unit Price = Total Cost ÷ Number of Items
Calculation: $4.00 ÷ 8 = $0.50
Answer: $0.50 per pencil
Example 2: 5 pounds of apples cost $7.50. What is the unit price per pound?
Calculation: $7.50 ÷ 5 = $1.50
Answer: $1.50 per pound
Example 3: Comparing Prices
Which is a better deal?
• Brand A: 6 cookies for $3.00
• Brand B: 10 cookies for $4.50
Brand A: $3.00 ÷ 6 = $0.50 per cookie
Brand B: $4.50 ÷ 10 = $0.45 per cookie
Answer: Brand B is the better deal ($0.45 < $0.50)
11. Find the Number of Each Type of Coin
U.S. 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 or 100¢ |
Strategy for Coin Problems
Step 1: Identify what you know (total value, total number of coins, or relationships)
Step 2: Set up equations using coin values
Step 3: Use trial and error or algebra
Step 4: Check that your answer matches all conditions
Example
"You have 8 coins that total $1.00. The coins are only quarters and nickels. How many of each coin do you have?"
Let's try combinations:
Total coins = 8, Total value = $1.00 (100¢)
Try 1: 4 quarters, 4 nickels
• Quarters: 4 × 25¢ = 100¢
• Nickels: 4 × 5¢ = 20¢
• Total: 120¢ ✗ (Too much)
Try 2: 3 quarters, 5 nickels
• Quarters: 3 × 25¢ = 75¢
• Nickels: 5 × 5¢ = 25¢
• Total: 100¢ ✓ (Correct!)
Answer: 3 quarters and 5 nickels
12. Convert Time Units
Time Conversion Chart
Unit Conversion | Formula |
---|---|
1 minute | 60 seconds |
1 hour | 60 minutes |
1 hour | 3,600 seconds |
1 day | 24 hours |
1 week | 7 days |
1 year | 12 months |
1 year | 52 weeks |
1 year | 365 days (366 in leap year) |
Conversion Rules
Large Unit → Small Unit: MULTIPLY
Small Unit → Large Unit: DIVIDE
Conversion Formulas
Minutes to Seconds: Minutes × 60 = Seconds
Seconds to Minutes: Seconds ÷ 60 = Minutes
Hours to Minutes: Hours × 60 = Minutes
Minutes to Hours: Minutes ÷ 60 = Hours
Days to Hours: Days × 24 = Hours
Hours to Days: Hours ÷ 24 = Days
Weeks to Days: Weeks × 7 = Days
Days to Weeks: Days ÷ 7 = Weeks
Examples
Example 1: Convert 5 minutes to seconds
Formula: Minutes × 60 = Seconds
Calculation: 5 × 60 = 300 seconds
Example 2: Convert 180 minutes to hours
Formula: Minutes ÷ 60 = Hours
Calculation: 180 ÷ 60 = 3 hours
Example 3: Convert 3 hours to seconds
Step 1: Hours to minutes: 3 × 60 = 180 minutes
Step 2: Minutes to seconds: 180 × 60 = 10,800 seconds
OR use direct formula: 3 × 3,600 = 10,800 seconds
Example 4: Convert 2 weeks to days
Formula: Weeks × 7 = Days
Calculation: 2 × 7 = 14 days
Example 5: Convert 48 hours to days
Formula: Hours ÷ 24 = Days
Calculation: 48 ÷ 24 = 2 days
Quick Reference Summary
Money Operations
• Add/Subtract: Line up decimal points
• Multiply: Total Cost = Price × Quantity
• Divide: Unit Price = Total ÷ Quantity
• Always write money with $ and two decimal places
Coin Values (Memorize!)
• Penny = 1¢ | Nickel = 5¢ | Dime = 10¢ | Quarter = 25¢
Time Conversions (Memorize!)
• 1 min = 60 sec | 1 hr = 60 min | 1 day = 24 hrs | 1 week = 7 days
💡 Important Tips to Remember
✓ Money always has 2 decimal places ($5.00, not $5)
✓ Line up decimal points when adding or subtracting money
✓ Unit price helps compare which item is a better deal
✓ Quarter = 25¢ is the most commonly used coin in word problems
✓ 60 is the magic number for time (60 seconds, 60 minutes)
✓ Larger to smaller units → Multiply
✓ Smaller to larger units → Divide
✓ Always include units in your answer (dollars, hours, etc.)
Master Money and Time! 💰⏰
Practice daily with real-life situations - shopping, cooking, and planning!