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Math · Money & Number Sense
Money Problems: Total Cost, Change, Unit Price and a Reasonableness Check
Solve meaningful Canadian dollar-and-cent problems: combine prices, compare per-item cost, plan a small budget and use estimates to catch mistakes.
The idea
A price has units. $4.05 means four dollars and five cents, not four dollars and fifty cents. When writing a calculation, place the decimal points so cents stay with cents.
Before calculating exactly, ask whether the answer should be smaller or larger than the money available. A quick estimate can expose an extra zero or a missing dollar.
Total price answers 'How much for everything?' Unit price answers 'How much for one item?' The cheaper package may not have the lower unit price when the quantities differ.
All prices in this lesson are invented practice examples without taxes, fees or cash-rounding rules. Real shop prices may include additional conditions; read the displayed terms before buying.
Worked examples
Example 1 · Add two prices
A notebook costs $3.75 and a folder costs $2.60. How much together?
- Estimate: about $4 + $3 = $7.
- Add cents: 75¢ + 60¢ = 135¢ = $1.35.
- Add dollars: $3 + $2 + $1.35 = $6.35.
- Check: $6.35 is a little below the $7 estimate.
$6.35.
Example 2 · Find change
You have $20.00 and select items worth $13.65. How much remains?
- Subtract the cost from the money available.
- 20.00 − 13.65 = 6.35.
- Check: 13.65 + 6.35 = 20.00.
$6.35 remains.
Example 3 · Compare a pack
A pack of three pens costs $5.40. An identical single pen costs $1.95. Which costs less per pen?
- Compute the pack's unit cost: $5.40 ÷ 3.
- Each pack pen costs $1.80.
- Compare $1.80 with $1.95 for the same item.
- The pack saves 15 cents per pen, but only if you need all three.
The three-pack, at $1.80 per pen.
Example 4 · Reject a tempting shortcut
Four books cost $3.25 each. Someone adds 4 + 3.25 and obtains $7.25.
- Four is a quantity of books, not a price.
- Equal groups require multiplication: 4 × $3.25.
- 3.25 × 4 = 13.00.
- A rough check: four items near $3 each should cost around $12, not $7.
$13.00, not $7.25.
Example 5 · Budget and explain
With $25, can you buy two $8.50 books and a $4.25 notebook?
- Two books cost 2 × $8.50 = $17.00.
- Total before any extra charges: $17.00 + $4.25 = $21.25.
- Budget remaining: $25.00 − $21.25 = $3.75.
- The answer is positive, so these invented prices fit within the practice budget.
Yes; $3.75 remains.
Common mistakes
These are tempting because they use familiar operations. Check what the question is actually measuring.
Why this fails: If you buy three identical items, multiply the unit price by three. Quantity is not automatically a price.
Why this fails: Two packages of different sizes must be compared on the same basis, such as price per one identical item.
Why this fails: 100 cents make one dollar; writing $4.100 is not proper money notation.
Why this fails: All amounts are classroom examples and exclude unspecified real-world conditions.
Foundation
Foundation practice
Read cents and combine small amounts accurately.
1. Write $6.40 in dollars and cents.
2. Which is greater: $4.09 or $4.90?
3. A pencil is $2.00 and a notebook is $3.50. What is the total?
4. Two erasers cost $1.25 each. Find the total.
5. You pay $10.00 for a $6.25 item. What change is due?
6. Is $8 enough for three items that cost $2.90 each?
7. Why should you write $0.75 rather than $75 for seventy-five cents?
Calculate and compare
Calculate and compare practice
Find totals, change and per-item amounts.
8. A ruler is $1.80 and a pen is $2.65. What is the total?
9. Three journals cost $4.20 each. What is the total?
10. A $20.00 note pays for books worth $13.40. How much change?
11. Which is cheaper: two pens at $1.75 each or a $3.20 two-pack?
12. A four-pack costs $6.00 and one item costs $1.80. Which is the lower per-item price?
13. Estimate $7.90 + $3.15 to the nearest whole dollar, then find the exact total.
14. A $5.00 bookmark and two $2.25 pencils cost how much?
Use a budget
Use a budget practice
Use a multi-step plan and defend the operation.
15. A student buys three $2.50 stickers and a $4.00 notebook. What is the total?
16. You have $15.00 and select items totalling $12.85. How much remains?
17. Two books cost $4.75 each. You pay $10.00. What is the change?
18. A child adds $2.50 + $2.50 and says $4.100. Explain the error.
19. Three identical markers for $5.40 cost how much each?
20. Two notebooks for $7.00 or three for $9.60: which option has the lower unit price?
21. Why is the cheapest total not always the lowest unit price?
Transfer and justify
Transfer and justify practice
Evaluate strategies, estimates and claims.
22. Is $50 enough for five $8.95 sets before any taxes or fees?
23. Why must you keep cents aligned when adding $5.80 and $0.45?
24. Give one combination of a $3 book and $2 pencil that totals exactly $12.
25. A shopper has $25.00 and buys two $6.75 items and one $3.40 item. What remains?
26. For four $2.50 items, compare repeated addition and multiplication.
27. A $12.00 total is reported for three $4.50 books. How can you show it is incorrect?
28. One pack has six pencils for $7.20. Another has four for $5.20. Which offers the lower unit price?
Answer key
- 1. 6 dollars and 40 cents
The decimal separates the dollar amount from the two cent digits. - 2. $4.90
Both have four dollars; ninety cents is more than nine cents. - 3. $5.50
Add the dollar and cent amounts: 2.00 + 3.50 = 5.50. - 4. $2.50
1.25 + 1.25 = 2.50. - 5. $3.75
10.00 − 6.25 = 3.75. - 6. No
Three times about three dollars is about nine dollars; exactly 3 × 2.90 = 8.70. - 7. $0.75 shows a fraction of a dollar
Seventy-five cents is less than one dollar; $75 is seventy-five whole dollars. - 8. $4.45
1.80 + 2.65 = 4.45. - 9. $12.60
4.20 × 3 = 12.60. - 10. $6.60
20.00 − 13.40 = 6.60. - 11. The $3.20 two-pack, by $0.30
Two individual pens cost $3.50; 3.50 − 3.20 = 0.30. - 12. The four-pack, at $1.50 each
6.00 ÷ 4 = 1.50, less than 1.80. - 13. About $11; exactly $11.05
Rounded: 8 + 3 = 11. Exact: 7.90 + 3.15 = 11.05. - 14. $9.50
Two pencils cost $4.50; add the $5.00 bookmark. - 15. $11.50
3 × 2.50 = 7.50; 7.50 + 4.00 = 11.50. - 16. $2.15
15.00 − 12.85 = 2.15. - 17. $0.50
2 × 4.75 = 9.50; 10.00 − 9.50 = 0.50. - 18. The correct total is $5.00
Fifty cents plus fifty cents is one whole dollar; regroup cents into dollars. - 19. $1.80 each
5.40 ÷ 3 = 1.80. - 20. Three for $9.60
7.00 ÷ 2 = 3.50 each; 9.60 ÷ 3 = 3.20 each. - 21. The packages may contain different quantities
Compare cost per one item when amounts differ. - 22. Yes
5 × 8.95 = 44.75, which is below $50. - 23. To add equal place values
The total is $6.25: forty-five cents is added to eighty cents, with regrouping. - 24. Two books and three pencils
2 × 3 + 3 × 2 = 12; other correct combinations may exist. - 25. $8.10
2 × 6.75 + 3.40 = 16.90; 25.00 − 16.90 = 8.10. - 26. Both give $10.00
2.50 + 2.50 + 2.50 + 2.50 = 4 × 2.50 = 10.00. - 27. 3 × $4.50 = $13.50
Multiply the unit cost by three and compare with $12.00. - 28. Six for $7.20
7.20 ÷ 6 = 1.20 per pencil; 5.20 ÷ 4 = 1.30.