Solved Exercises on Making Change in Grade 2

Master making change: calculating money returned, subtraction skills, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic change calculation
Exercise 1
You buy a candy bar for $0.75. You give the cashier $1.00. How much change should you get back?
Definition:

Making change: The process of calculating the money returned to a customer when they pay more than the cost of an 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. Verify your answer by adding cost + change
$1.00
Paid
→
$0.75
Cost
+
$0.25
Change
Step 1: Identify what you paid

You gave $1.00 to the cashier

Step 2: Identify the cost

The candy bar costs $0.75

Step 3: Subtract to find the change

$1.00 - $0.75 = $0.25

Step 4: Verify your answer

Cost + Change = Amount Paid

$0.75 + $0.25 = $1.00 ✓

Change: $0.25
Final answer:

You should get $0.25 in change back.

Applied rules:

• Subtraction: Amount Paid - Cost = Change

• Verification: Cost + Change should equal amount paid

• Real-world application: Understanding money transactions

2 Medium difficulty
Exercise 2
You buy a book for $3.25. You pay with a $5 bill. How much change do you receive?
Definition:

Change breakdown: The specific coins and bills that make up the change amount.

$5.00
Paid
→
$3.25
Cost
+
$1.75
Change
Step 1: Identify the amount paid

You paid with a $5.00 bill

Step 2: Identify the cost

The book costs $3.25

Step 3: Calculate the change

$5.00 - $3.25 = $1.75

Step 4: Break down the change (optional)

$1.75 could be: $1 bill + 3 quarters, or 7 quarters, etc.

Step 5: Verify your answer

$3.25 + $1.75 = $5.00 ✓

Change: $1.75
Final answer:

You should receive $1.75 in change.

Applied rules:

• Subtraction: Larger amount - smaller amount = difference

• Verification: Always check by adding cost + change

• Breakdown flexibility: Same amount can be given in different combinations

3 Complex transaction
Exercise 3
You buy stickers for $1.10 and a pencil for $0.45. You give the cashier $2.00. How much change do you get?
Definition:

Multiple items: When buying more than one item, add the costs together before calculating change.

$2.00
Paid
→
$1.55
Total Cost
+
$0.45
Change
Step 1: Add up the costs

Stickers: $1.10 + Pencil: $0.45 = $1.55 total

Step 2: Identify the amount paid

You gave $2.00

Step 3: Calculate the change

$2.00 - $1.55 = $0.45

Step 4: Verify your answer

$1.55 + $0.45 = $2.00 ✓

Change: $0.45
Final answer:

You should get $0.45 in change.

Applied rules:

• Multiple items: Add costs first, then subtract from payment

• Sequential operations: Addition followed by subtraction

• Verification: Check that cost + change = amount paid

Rules and methods, laws,...
\text{Change} = \text{Amount Paid} - \text{Total Cost}
Change Formula
Formula 1
\text{Change} = \text{Paid} - \text{Cost}
Basic change formula
Formula 2
\text{Total Cost} = \sum \text{Item Costs}
For multiple items
Formula 3
\text{Paid} = \text{Cost} + \text{Change}
Verification formula
Key definitions:

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

Total Cost: The sum of prices for all items bought

Amount Paid: The money given to the cashier

Verification: Checking that your calculation is correct

Complete change-making methodology:
  1. Identify costs: Find the price of each item
  2. Calculate total: Add up all costs if multiple items
  3. Identify payment: Note how much money was given
  4. Subtract: Payment - Total Cost = Change
  5. Verify: Check that Total Cost + Change = Payment
Tip 1: Always add up costs first when buying multiple items.
Tip 2: Check your answer by adding the cost and change to see if it equals what you paid.
Tip 3: Change is always positive (you can't get negative change).
Tip 4: If you don't have exact change, you might get a receipt showing the amount owed.
Common errors: Forgetting to add multiple item costs, subtracting the wrong way (cost - payment instead of payment - cost), not verifying answers.
Memory aids: "Paid minus Cost equals Change" - helps remember the order of subtraction.
Rules to know by heart:

• Change = Amount Paid - Total Cost

• Total Cost = Sum of all item prices

• Verification: Cost + Change = Amount Paid

• You must pay at least as much as the total cost

Solution: Exercises 4 to 5
4 Real-world scenario
Exercise 4
At the store, you buy a toy car for $2.85, a pack of gum for $0.75, and a notebook for $1.20. You give the cashier a $10 bill. How much change do you get?
Definition:

Real-world application: Using change-making skills in actual shopping situations with multiple items and larger amounts.

$10.00
Paid
→
$4.80
Total Cost
+
$5.20
Change
Step 1: Add up all item costs

Toy car: $2.85 + Gum: $0.75 + Notebook: $1.20 = $4.80

Step 2: Identify the amount paid

You gave a $10.00 bill

Step 3: Calculate the change

$10.00 - $4.80 = $5.20

Step 4: Verify your answer

$4.80 + $5.20 = $10.00 ✓

Change: $5.20
Final answer:

You should receive $5.20 in change.

Applied rules:

• Multiple items: Add all costs before subtracting

• Large amounts: Same principle applies to bigger numbers

• Verification: Always check your calculation

5 Advanced problem
Exercise 5
You want to buy a game that costs $12.50. You have 2 five-dollar bills and 3 one-dollar bills. Do you have enough money? If yes, how much change will you get if you pay exactly what you need?
Definition:

Money sufficiency: Determining if you have enough money to make a purchase before calculating change.

$13.00
Have
→
$12.50
Cost
+
$0.50
Change
Step 1: Count your money

2 five-dollar bills = 2 × $5.00 = $10.00

3 one-dollar bills = 3 × $1.00 = $3.00

Total: $10.00 + $3.00 = $13.00

Step 2: Compare to the cost

You have $13.00 and the game costs $12.50

Since $13.00 > $12.50, you have enough money

Step 3: Calculate the change

If you pay exactly $12.50, you get $0.00 change

If you pay $13.00, you get $13.00 - $12.50 = $0.50 change

Step 4: Answer the questions

Yes, you have enough money. If you pay $13.00, you'll get $0.50 change.

Yes, $0.50 change if paying $13.00
Final answer:

Yes, you have enough money. You have $13.00 total, and the game costs $12.50. If you pay with your $13.00, you'll get $0.50 in change.

Applied rules:

• Sufficiency check: Money ≥ Cost = enough money

• Payment flexibility: You can pay exact amount or more

• Change calculation: Based on what you actually pay

Key Concepts and Memory Aids for Making Change
\text{Change} = \text{Paid} - \text{Cost}
Core Formula
Key definitions:

Change: The difference between money paid and the cost of items

Total Cost: Sum of all item prices when buying multiple things

Verification: Double-checking your calculation is correct

Sufficiency: Having enough money to make a purchase

Payment: The money given to complete a transaction

Step-by-step change-making methods:
  1. Assess: Look at all items and their prices
  2. Calculate: Add up total cost if multiple items
  3. Pay: Give money to the cashier
  4. Subtract: Paid amount - total cost = change
  5. Verify: Check that cost + change = paid amount
Memory trick: "Paid minus Cost equals Change" - the order matters in subtraction!
Verification habit: Always add cost + change to check if it equals what you paid.
Multiple items: Always add all costs together before calculating change.
Real-world skill: Making change is essential for shopping and financial literacy.
Common mistakes: Subtracting in wrong order (cost - paid instead of paid - cost), forgetting to add multiple item costs, not checking answers.
Quick facts: Change is always positive, total cost is always ≤ amount paid, verification is crucial for accuracy.
Essential rules to memorize:

• Change = Amount Paid - Total Cost

• Total Cost = Sum of all individual item costs

• Verification: Cost + Change = Amount Paid

• Sufficiency: Money ≥ Cost means you have enough

Making Change Infographic

💰
Formula

Change = Paid - Cost

Verification: Cost + Change = Paid

Multiple Items

Total Cost = Item1 + Item2 + Item3...

Then: Change = Paid - Total Cost

Verification

Always check: Cost + Change = Paid

This confirms your calculation is correct

Change-Making Process
1
Add costs
2
Note payment
3
Subtract
4
Verify

Questions & Answers

Question: Why do we subtract to find change? Shouldn't we add?

Answer: Great question! We subtract because change is the "leftover" money after paying for something.

Think of it like this:

  • You start with $1.00
  • You spend $0.75 on candy
  • How much do you have left? $1.00 - $0.75 = $0.25

We subtract because we're finding out what's "left over" after the purchase. Adding would give us more money than we started with, which doesn't make sense!

Remember: Change = What you paid - What the item cost.

Question: What happens if I don't have enough money to buy something?

Answer: If you don't have enough money, you cannot buy the item. Here's what happens:

  • The cashier will tell you that you need more money
  • You'll need to put the item back or find something cheaper
  • Or you can ask someone to lend you money

For example, if a toy costs $5.00 but you only have $3.00:

$3.00 is less than $5.00, so you don't have enough money.

You would need $5.00 - $3.00 = $2.00 more to buy the toy.

This is why it's important to count your money before trying to buy something!

Question: How do I know if my change calculation is correct?

Answer: There's a simple way to check if your change calculation is correct:

Add the cost and the change together. If the sum equals what you paid, your calculation is correct!

For example:

  • Item costs $0.75
  • You paid $1.00
  • Your change is $0.25

Check: $0.75 + $0.25 = $1.00 ✓

This works because: Cost + Change = Amount Paid

This verification step is very important and helps catch mistakes!