Solved Exercises on Comparing Money Amounts in Grade 3

Master comparing money amounts: using greater than, less than, equal to, converting dollars and cents, ordering money amounts, and solving comparison word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic money comparison
Exercise 1
Compare $2.50 and $2.75. Which amount is greater? Use the appropriate symbol (<, >, or =).
Definition:

Comparing money amounts: Determining which of two or more money amounts is greater, lesser, or equal. Use symbols: < (less than), > (greater than), = (equal to).

Comparison method:
  1. Look at the dollar amounts first
  2. If dollars are equal, compare the cents
  3. Use the appropriate comparison symbol
Amount 1
$2.50
Amount 2
$2.75
Comparison
$2.50 < $2.75
Step 1: Compare the dollars

Both amounts have $2 in dollars, so dollars are equal

Step 2: Compare the cents

50¢ vs 75¢. Since 50 < 75, $2.50 is less than $2.75

Step 3: Use the comparison symbol

$2.50 < $2.75

Step 4: State the answer

$2.75 is greater than $2.50

$2.50 < $2.75
Final answer:

$2.50 < $2.75, so $2.75 is greater

Applied rules:

• Compare dollars first: If different, the one with more dollars is greater

• Compare cents second: Only if dollars are equal

• Symbol direction: The open side of < or > points to the greater amount

2 Converting and comparing
Exercise 2
Compare 350 cents and $3.45. Which amount is greater? Convert to the same unit before comparing.
Definition:

Unit conversion: Converting money amounts to the same unit (dollars or cents) before comparing them.

350 cents
= $3.50
Other amount
$3.45
Comparison
$3.50 > $3.45
Step 1: Convert to same unit

Convert 350 cents to dollars: 350 ÷ 100 = $3.50

Step 2: Compare the converted amounts

Now compare $3.50 and $3.45

Step 3: Compare the cents

Dollars are equal ($3), so compare cents: 50¢ > 45¢

Step 4: State the comparison

$3.50 > $3.45, so 350 cents > $3.45

350 cents > $3.45
Final answer:

350 cents is greater than $3.45

Applied rules:

• Unit conversion: Convert to same units before comparing

• Conversion factor: 100 cents = 1 dollar

• Comparison: Once in same units, compare normally

3 Ordering money amounts
Exercise 3
Order these amounts from least to greatest: $1.25, $0.98, $1.05, $1.30
Definition:

Ordering money amounts: Arranging a set of money amounts from least to greatest (ascending) or greatest to least (descending).

All amounts
$0.98, $1.05, $1.25, $1.30
Step 1: Compare dollars first

$0.98 has 0 dollars, others have 1 dollar, so $0.98 is smallest

Step 2: Compare remaining amounts

Compare $1.05, $1.25, $1.30 (all have $1)

Step 3: Compare the cents

For $1.05, $1.25, $1.30: 05¢ < 25¢ < 30¢

Step 4: Order from least to greatest

$0.98 < $1.05 < $1.25 < $1.30

$0.98, $1.05, $1.25, $1.30
Final answer:

From least to greatest: $0.98, $1.05, $1.25, $1.30

Applied rules:

• Compare dollars first: Sort by dollar amounts initially

• Compare cents second: When dollars are equal, compare cents

• Ascending order: From smallest to largest

Rules and methods, laws,...
100¢ = $1.00
Money Conversion
Comparison Symbols
> Greater Than
Open side points to larger amount
Comparison Symbols
< Less Than
Pointed side faces smaller amount
Comparison Symbols
= Equal To
Same value on both sides
Key definitions:

Money comparison: Determining which of two or more amounts is greater, lesser, or equal using <, >, or = symbols.

Greater than (>): Used when the first amount is larger than the second amount.

Less than (<): Used when the first amount is smaller than the second amount.

Equal to (=): Used when both amounts have the same value.

Ordering: Arranging amounts from least to greatest or greatest to least.

Unit conversion: Converting between dollars and cents to compare amounts.

Comparing money methodology:
  1. Check units: Ensure both amounts are in same unit (dollars or cents)
  2. Compare dollars: If different, the one with more dollars is greater
  3. Compare cents: If dollars are equal, compare the cents
  4. Select symbol: Use <, >, or = appropriately
Tip 1: Always convert to the same unit before comparing different formats.
Tip 2: Remember: 100 cents = 1 dollar for conversions.
Tip 3: Compare dollars first, then cents if dollars are equal.
Tip 4: The open side of < or > always faces the larger amount.
Common errors: Comparing different units without conversion, confusing < and > symbols, forgetting that 100 cents = 1 dollar, comparing cents before dollars.
Real-world applications: Shopping comparisons, budgeting, price checking, making change, financial planning.
Formulas to know by heart:

• 100 cents = 1 dollar

• To convert cents to dollars: divide by 100

• To convert dollars to cents: multiply by 100

• Comparison order: dollars first, then cents

• Symbol direction: open side toward greater amount

Solution: Exercises 4 to 5
4 Real-world comparison
Exercise 4
Sarah has $5.25 and Tom has 530 cents. Who has more money? How much more?
Definition:

Real-world comparison: Applying money comparison skills to practical scenarios involving different people's money amounts.

Sarah's money
$5.25
Tom's money
530¢ = $5.30
Difference
$5.30 - $5.25 = $0.05
Step 1: Convert to same unit

Convert 530 cents to dollars: 530 ÷ 100 = $5.30

Step 2: Compare the amounts

$5.25 vs $5.30. Dollars are equal, so compare cents: 25¢ < 30¢

Step 3: Determine who has more

Tom has more money since $5.30 > $5.25

Step 4: Calculate the difference

$5.30 - $5.25 = $0.05 (5 cents)

Step 5: State the answer

Tom has 5 cents more than Sarah

Tom has more by 5 cents
Final answer:

Tom has more money. He has 5 cents more than Sarah.

Applied rules:

• Unit conversion: Convert different formats to same unit

• Comparison: Compare after converting to same unit

• Difference: Subtract smaller amount from larger to find how much more

5 Multi-step comparison word problem
Exercise 5
Emma has $3.40. She wants to buy a book that costs $3.75. Does she have enough money? If not, how much more does she need?
Definition:

Budget comparison: Comparing available funds with required cost to determine if purchase is possible and calculate any shortage.

Emma's money
$3.40
Book cost
$3.75
Shortage
$3.75 - $3.40 = $0.35
Step 1: Identify the amounts to compare

Emma has $3.40, book costs $3.75

Step 2: Compare the amounts

$3.40 vs $3.75. Since 3.40 < 3.75, Emma doesn't have enough

Step 3: Calculate how much more is needed

Subtract what she has from what she needs: $3.75 - $3.40 = $0.35

Step 4: State the answer

Emma needs 35 cents more to buy the book

Step 5: Verify the calculation

$3.40 + $0.35 = $3.75 ✓

Emma needs $0.35 more
Final answer:

Emma does not have enough money. She needs $0.35 more to buy the book.

Applied rules:

• Comparison: Compare available funds with required cost

• Shortage calculation: Subtract available from required to find difference

• Verification: Check that available + shortage = required

Complete Summary: Comparing Money Amounts
100¢ = $1.00
Money Conversion
Key definitions:

Money comparison: Determining which of two or more money amounts is greater, lesser, or equal using comparison symbols (<, >, =).

Greater than (>): Indicates the first amount is larger than the second amount. The open side of the symbol faces the larger amount.

Less than (<): Indicates the first amount is smaller than the second amount. The pointed side of the symbol faces the smaller amount.

Equal to (=): Indicates both amounts have the same value.

Unit conversion: Changing money amounts from one format to another (cents to dollars or vice versa) to facilitate comparison.

Ordering: Arranging a set of money amounts in ascending (least to greatest) or descending (greatest to least) order.

Budget comparison: Comparing available funds with required costs to determine if a purchase is possible.

Complete comparison methodology:
  1. Check units: Ensure all amounts are in the same unit (convert if necessary)
  2. Compare dollars: If dollar amounts differ, the one with more dollars is greater
  3. Compare cents: If dollar amounts are equal, compare the cents
  4. Apply symbol: Use the appropriate comparison symbol (<, >, =)
  5. Verify: Double-check your comparison makes logical sense
Tip 1: Always convert different formats to the same unit before comparing (e.g., convert cents to dollars).
Tip 2: Remember the conversion: 100 cents = 1 dollar.
Tip 3: Compare dollar amounts first, then cents if dollars are equal.
Tip 4: The open side of < or > always points to the greater amount.
Tip 5: When ordering multiple amounts, sort by dollars first, then by cents.
Common errors: Comparing different units without conversion, confusing the direction of < and > symbols, forgetting that 100 cents equals 1 dollar, comparing cents before checking if dollars are equal.
Real-world applications: Shopping (comparing prices), budgeting (checking if you have enough money), making change, saving money, financial planning, price matching.
Key formulas and facts:

• 100 cents = 1 dollar

• To convert cents to dollars: divide by 100

• To convert dollars to cents: multiply by 100

• Comparison order: dollars first, then cents

• Symbol direction: open side toward greater amount

• Ascending order: least to greatest

• Descending order: greatest to least

• Budget check: Available ≥ Required for purchase to be possible

Visual Guide to Comparing Money Amounts

💰
Comparison Symbols

> Greater Than: Open side faces larger amount

< Less Than: Pointed side faces smaller amount

= Equal To: Both sides have same value

Example: $2.50 < $2.75

Unit Conversion

100 cents = 1 dollar

To convert cents to dollars: divide by 100

To convert dollars to cents: multiply by 100

Example: 250¢ = $2.50

Comparison Strategy

1. Convert to same units

2. Compare dollars first

3. If dollars equal, compare cents

4. Use appropriate symbol

Ordering Money

Sort by dollars first

Then by cents (if dollars equal)

Ascending: least to greatest

Descending: greatest to least

Example: $1.25, $1.50, $2.00

Questions & Answers

Question: I get confused about which way the < and > symbols point. How can I remember which is which?

Answer: Here are some helpful ways to remember:

  • Alligator method: Think of the symbol as an alligator's mouth that always wants to eat the bigger number
  • Open side rule: The open side of the symbol always faces the greater amount
  • Pointed side rule: The pointed side always faces the smaller amount

Example: $3.50 > $2.75 - The open side faces $3.50 (the bigger amount)

Example: $1.25 < $2.00 - The open side faces $2.00 (the bigger amount)

Practice with different amounts until the symbol direction becomes natural!

Question: When comparing money amounts like $1.25 and $1.05, should I look at the dollars or cents first?

Answer: Always compare the dollars first, then the cents only if the dollars are equal:

  • Step 1: Compare the dollar amounts ($1 vs $1 in your example)
  • Step 2: If dollars are equal, compare the cents (25¢ vs 05¢)
  • Step 3: Make your decision based on the comparison

In your example: $1.25 vs $1.05

Dollars are equal ($1 = $1), so compare cents: 25¢ > 5¢, therefore $1.25 > $1.05

This method works consistently for all money comparisons!

Question: I see problems with both dollars and cents mixed, like $2.50 and 275 cents. How do I compare these?

Answer: When comparing different formats, you must convert them to the same unit first:

  • Option 1: Convert cents to dollars (divide by 100)
  • Option 2: Convert dollars to cents (multiply by 100)

Example: Compare $2.50 and 275 cents

Method 1: Convert 275 cents to dollars: 275 ÷ 100 = $2.75

Now compare: $2.50 vs $2.75 → $2.50 < $2.75

Method 2: Convert $2.50 to cents: $2.50 × 100 = 250 cents

Now compare: 250 cents vs 275 cents → 250 < 275

Both methods give the same result: $2.50 < 275 cents

Always convert to the same unit before comparing!