Solved Exercises on Making Change in Grade 3

Master making change: counting money, calculating change, using coins and bills, making change with regrouping, and solving word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic change calculation
Exercise 1
You buy a toy that costs $3.75. You give the cashier $5.00. How much change should you receive?
Definition:

Making change: Calculating the difference between the amount paid and the cost of an item. Change = Amount Paid - Cost of Item.

Change calculation method:
  1. Identify the cost of the item
  2. Identify the amount paid
  3. Subtract the cost from the amount paid
  4. Count out the change using coins and bills
Amount paid
$5.00
Cost
$3.75
Change
$5.00 - $3.75 = $1.25
Step 1: Identify the amounts

Item cost: $3.75, Amount paid: $5.00

Step 2: Set up the subtraction

$5.00 - $3.75 = ?

Step 3: Subtract the cents first

0.00 - 0.75: Need to borrow from dollars. 0.00 becomes 1.00, 5 becomes 4

Step 4: Complete the subtraction

4.00 - 3.00 = 1.00, and 1.00 - 0.75 = 0.25. So 1.00 + 0.25 = 1.25

Change = $1.25
Final answer:

You should receive $1.25 in change

Applied rules:

• Change formula: Change = Amount Paid - Cost

• Borrowing: When subtracting cents, borrow from dollars if needed

• Verification: Cost + Change should equal Amount Paid ($3.75 + $1.25 = $5.00)

2 Making change with coins
Exercise 2
A candy bar costs 87 cents. You pay with $1.00. Show how to make the change using the fewest coins possible.
Definition:

Coin denominations: Penny (1¢), Nickel (5¢), Dime (10¢), Quarter (25¢). To make change with fewest coins, use largest denominations first.

Amount paid
$1.00 = 100¢
Cost
87¢
Change
100¢ - 87¢ = 13¢
Step 1: Calculate the change amount

$1.00 - 87¢ = 100¢ - 87¢ = 13¢

Step 2: Use largest coins first

With 13¢, try quarters (25¢) - too big, so skip

Step 3: Try dimes (10¢)

One dime (10¢) leaves 3¢ remaining

Step 4: Make up remaining amount

With 3¢ left, use 3 pennies (1¢ each)

Step 5: Count total coins

1 dime + 3 pennies = 4 coins total (the fewest possible)

Change: 1 dime and 3 pennies = 13¢
Final answer:

The change is 13 cents: 1 dime and 3 pennies (4 coins total)

Applied rules:

• Coin values: Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢

• Fewest coins: Use largest denominations first

• Verification: 10¢ + 3¢ = 13¢ ✓

3 Making change with regrouping
Exercise 3
You buy a book for $4.89. You give the cashier $10.00. Calculate the change using regrouping.
Definition:

Regrouping: Borrowing from higher place values when subtracting. When subtracting money, regroup from dollars to cents if needed.

Amount paid
$10.00
Cost
$4.89
Change
$10.00 - $4.89 = $5.11
Step 1: Write the subtraction vertically

$10.00 - $4.89

Step 2: Regroup from dollars to cents

We need to subtract 9¢ from 0¢. Borrow 1 dollar (100¢): $10.00 becomes $9.100

Step 3: Continue regrouping

Now we have $9.99 (after borrowing 1¢ for the hundredths place)

Step 4: Subtract column by column

From right to left: 100¢ - 89¢ = 11¢, 9 - 4 = 5 dollars

Step 5: Combine results

5 dollars and 11 cents = $5.11

Change = $5.11
Final answer:

The change is $5.11

Applied rules:

• Regrouping: Borrow from higher place values when subtracting

• Money subtraction: Treat dollars and cents separately but with borrowing

• Verification: $4.89 + $5.11 = $10.00 ✓

Rules and methods, laws,...
Change = Amount Paid - Cost
Change Formula
Coin Values
Quarter = 25¢
Value of a quarter
Coin Values
Dime = 10¢
Value of a dime
Coin Values
Nickel = 5¢
Value of a nickel
Key definitions:

Change: The money returned to a customer when they pay more than the cost of an item

Amount paid: The total money given to the cashier

Cost: The price of the item(s) purchased

Coin: Small denomination money (penny, nickel, dime, quarter)

Bill: Paper money (one, five, ten, twenty dollar bills)

Regrouping: Borrowing from higher place values when subtracting

Making change methodology:
  1. Identify amounts: Note the cost and amount paid
  2. Subtract: Amount paid minus cost equals change
  3. Count coins: Start with largest denominations first
  4. Verify: Check that cost + change equals amount paid
Tip 1: Always subtract: Amount Paid - Cost = Change
Tip 2: Use largest coins first to make change with fewer coins
Tip 3: When subtracting money, regroup from dollars to cents if needed
Tip 4: Verify your answer: Cost + Change = Amount Paid
Common errors: Subtracting in wrong order, forgetting to regroup, counting coins incorrectly, not verifying the answer.
Real-world applications: Shopping, banking, vending machines, restaurants, market transactions.
Formulas to know by heart:

• Change = Amount Paid - Cost

• Cost + Change = Amount Paid

• Amount Paid - Change = Cost

• Coin values: Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢

• To minimize coins: Use largest denominations first

Solution: Exercises 4 to 5
4 Multiple items and change
Exercise 4
Sarah buys a notebook for $2.45, a pen for $1.20, and an eraser for $0.85. She pays with a $10 bill. How much change should she receive?
Definition:

Total cost: The sum of all individual item prices. When purchasing multiple items, add all costs before calculating change.

Notebook
$2.45
Pen
$1.20
Eraser
$0.85
Total
$4.50
Step 1: Calculate total cost

$2.45 + $1.20 + $0.85 = $4.50

Step 2: Identify amount paid

Sarah paid with a $10 bill

Step 3: Calculate change

$10.00 - $4.50 = $5.50

Step 4: Express change in bills and coins

$5.50 could be: one $5 bill and two quarters, or other combinations

Step 5: Verify the answer

$4.50 + $5.50 = $10.00 ✓

Total cost = $4.50, Change = $5.50
Final answer:

Sarah should receive $5.50 in change

Applied rules:

• Total cost: Add all individual prices first

• Change calculation: Amount paid minus total cost

• Verification: Total cost + Change = Amount paid

5 Word problem with multiple steps
Exercise 5
Tom has $20.00. He buys a video game for $14.99 and a controller for $8.45. Does he have enough money? If not, how much more does he need? If yes, how much change will he receive?
Definition:

Budget calculation: Comparing available funds with total expenses to determine if purchase is possible and the resulting balance.

Available money
$20.00
Video game
$14.99
Controller
$8.45
Total cost
$14.99 + $8.45 = $23.44
Step 1: Calculate total cost of purchases

$14.99 + $8.45 = $23.44

Step 2: Compare with available money

Tom has $20.00, but needs $23.44

Step 3: Determine if purchase is possible

Since $23.44 > $20.00, Tom does not have enough money

Step 4: Calculate how much more is needed

$23.44 - $20.00 = $3.44 more needed

Step 5: State the final answer

Tom needs $3.44 more to buy both items

Tom needs $3.44 more
Final answer:

Tom does not have enough money. He needs $3.44 more to buy both items.

Applied rules:

• Budgeting: Compare available funds with total expenses

• Shortage calculation: If expenses exceed funds, subtract to find how much more is needed

• Verification: Available + Needed = Total Cost

Complete Summary: Making Change
Change = Amount Paid - Cost
Change Formula
Key definitions:

Change: The money returned to a customer when they pay more than the cost of an item (Change = Amount Paid - Cost).

Amount paid: The total money given to the cashier to complete a purchase.

Cost: The price of the item(s) being purchased.

Coin: Small denomination currency (penny = 1¢, nickel = 5¢, dime = 10¢, quarter = 25¢).

Bill: Paper currency (one, five, ten, twenty dollar bills).

Regrouping: Borrowing from higher place values when performing subtraction (needed when subtracting cents).

Total cost: The sum of all individual item prices when purchasing multiple items.

Complete methodology:
  1. Identify amounts: Note the cost of items and the amount paid
  2. Calculate total cost: If multiple items, add all prices together
  3. Subtract: Amount paid minus total cost equals change
  4. Regroup if needed: Borrow from dollars to cents when subtracting
  5. Count coins: Use largest denominations first for fewest coins
  6. Verify: Check that cost + change equals amount paid
Tip 1: Always subtract: Amount Paid - Cost = Change (not the other way around).
Tip 2: When making change with coins, start with the largest denominations (quarters, then dimes, etc.).
Tip 3: When subtracting money and you need to borrow, convert 1 dollar to 100 cents.
Tip 4: Always verify your answer: Cost + Change should equal Amount Paid.
Tip 5: For multiple items, add all costs first, then subtract from the amount paid.
Common errors: Subtracting in wrong order, forgetting to regroup when subtracting money, counting coins incorrectly, not adding all item costs before calculating change, failing to verify answers.
Real-world applications: Shopping at stores, using vending machines, paying for food, banking transactions, budgeting, managing allowance.
Key formulas and facts:

• Change = Amount Paid - Cost

• Cost + Change = Amount Paid

• Amount Paid - Change = Cost

• Coin values: Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢

• To minimize coins: Use largest denominations first

• When regrouping: 1 dollar = 100 cents

• For multiple items: Add all costs first

Visual Guide to Making Change

💰
Change Formula

Change = Amount Paid - Cost

Example: Paid $10.00, Cost $3.75

Change = $10.00 - $3.75 = $6.25

Always verify: Cost + Change = Paid

Coin Values

Penny = 1¢ (smallest coin)

Nickel = 5¢

Dime = 10¢ (smallest in size)

Quarter = 25¢ (largest in size)

Use largest coins first!

Regrouping Strategy

When subtracting money:

If cents in payment < cents in cost

Borrow 1 dollar = 100 cents

Example: $5.00 - $2.85

Borrow to make $4.100 - $2.85

Multi-Item Purchases

1. Add all item costs first

2. Calculate total cost

3. Subtract from amount paid

4. Count change in coins/bills

5. Verify your calculation

Questions & Answers

Question: I sometimes get confused about which number to subtract from which when making change. Should I subtract the cost from the amount paid or the other way around?

Answer: Always subtract: Amount Paid - Cost = Change. Think of it this way:

  • The cashier starts with the money you gave them (amount paid)
  • They need to keep the cost of the item
  • The rest is given back to you as change

Example: You pay $5.00 for an item that costs $3.75. The cashier keeps $3.75 and gives you back $5.00 - $3.75 = $1.25.

If you subtracted the other way ($3.75 - $5.00), you'd get a negative number, which doesn't make sense for change!

Remember: You pay more than the cost, so subtract the smaller number (cost) from the larger number (amount paid).

Question: When making change with coins, why do we start with the biggest coins first? Can't I just use lots of pennies?

Answer: While you could use only pennies to make change, there are good reasons to use the largest coins first:

  • Efficiency: Fewer coins to count and handle
  • Convenience: Cashiers and customers prefer fewer coins
  • Standard practice: This is how real cashiers make change
  • Practicality: Carrying hundreds of pennies is difficult!

Example: To make 67¢, you could use 67 pennies, but it's much easier to use 2 quarters (50¢), 1 dime (10¢), 1 nickel (5¢), and 2 pennies (2¢) = 67¢ with only 6 coins instead of 67!

Using the fewest coins possible is the goal, which means starting with the largest denominations first.

Question: I get confused when I need to subtract money and have to borrow. Like when I need to subtract $3.85 from $5.00. Can you explain how to do this?

Answer: When subtracting money and you need to borrow, think of it as converting dollars to cents:

  • You have $5.00 but need to subtract 85¢ from 00¢
  • "Borrow" 1 dollar from the $5, which gives you 100¢
  • Now you have $4.00 + 100¢ = $4.100
  • Subtract the cents: 100¢ - 85¢ = 15¢
  • Subtract the dollars: $4 - $3 = $1
  • Total change: $1.15

Think of it like this: If you have 5 one-dollar bills and someone asks for 85 cents, you can break one dollar bill into 100 cents, then give them 85 cents and keep 15 cents.

Practice this with different amounts until it becomes natural. The key is remembering that 1 dollar = 100 cents when you need to borrow.