TACHS: Money with decimals: find the total, then the change
Find totals and change with dollars and cents, work back to an item's price from a receipt, compare pack prices and count how many items a budget buys.
How do you get money questions right when there are several items, decimals and a payment?
Short answer
Find the total cost first, then subtract it from the payment, lining up the decimal points. For a missing price, start from what was spent; for a budget, count only whole items.
Know first: Adding and subtracting decimals, Multiplying a decimal by a whole number
Step 1 of 6
A change question has two parts
To find change, you need the total cost first. Multiply the price by the number of items, add any other items, and only then subtract from the amount paid.
Most wrong answers come from stopping early (choosing the total) or from skipping a step (subtracting one item's price from the payment). Line up the decimal points every time you add or subtract.
| The question asks | First find | Then |
|---|---|---|
| How much change | Total cost | Payment − total |
| The price of one item on a receipt | Amount spent: payment − change | Subtract known items, divide by the count |
| Which pack is cheaper per item | Each pack's price ÷ its count | Subtract the two unit prices |
| How many whole items a budget buys | Budget ÷ price | Round down, multiply back, subtract for what is left |
Every row starts with a total or a unit price before anything else.
Step 2 of 6
Total, change, and a receipt worked backward
Worked example: Six juice bottles
Juice bottles cost $1.35 each. Priya buys 6 bottles and pays with a $10 bill. There is no tax. How much change does she get?
- A$1.90
- B$8.10
- C$8.65
- D$9.19
- 1
Find the total
6 × $1.00 = $6.00 and 6 × $0.35 = $2.10, so the total is $8.10.
- 2
Subtract from the payment
$10.00 − $8.10 = $1.90.
- 3
Estimate
Each bottle is a little under $1.50, so six cost a little under $9. The change should be a little over $1. $1.90 fits.
- 4
See why the other choices are there
$8.10 is the total, not the change. $8.65 subtracts the price of one bottle. $9.19 comes from misplacing the decimal and treating the total as $0.81.
Answer
Priya gets $1.90 in change.
Find the price of one drink
A sandwich costs $4.85. Ana also buys 4 identical drinks. She pays $15.00 and gets $3.15 back. There is no tax. What does each drink cost?
- 1
Amount spent: $15.00 − $3.15 = $11.85.
- 2
Split $11.85 among the 4 drinks: 11.85 ÷ 4 is about $2.96.
What went wrong
The $11.85 includes the $4.85 sandwich. Only part of it was spent on drinks.
- 3
Each drink costs about $2.96.
The fix
Take out the sandwich first: $11.85 − $4.85 = $7.00 for the drinks. Then $7.00 ÷ 4 = $1.75. Check: 4 × $1.75 + $4.85 + $3.15 = $15.00.
Step 3 of 6
Compare unit prices and spend a budget
To compare packs, find the price of one item in each. A pack of 4 for $3.00 is $0.75 each, and a pack of 6 for $4.20 is $0.70 each, so the 6-pack is $0.05 cheaper per item.
To see how many items a budget buys, divide and round down, since you cannot buy part of an item. With $15.00 and pens at $1.85: 8 pens cost $14.80 and 9 cost $16.65. So 8 pens, with $0.20 left.
Step 4 of 6
Total first, every time
Check yourself · Question 1
Erin buys 4 sketchbooks at $3.65 each. She pays with $25, and there is no tax. How much change should she get?
Answer: B
Total: 4 × $3.00 = $12.00 and 4 × $0.65 = $2.60, so $14.60. Change: $25.00 − $14.60 = $10.40.
Trap answer: $21.35
One item instead of the total
- Why it looks right
- The price $3.65 is printed right in the question, and $25 − $3.65 is a quick subtraction.
- Why it's wrong
- Erin bought 4 sketchbooks. Subtracting one price leaves out $10.95 she also spent.
- The right answer
- $10.40, because 4 × $3.65 = $14.60 and $25.00 − $14.60 = $10.40.
Check yourself · Question 2
Muffins are sold 3 for $4.20 or 5 for $6.25. How much less does one muffin cost in the 5-pack than in the 3-pack?
Answer: A
3-pack: $4.20 ÷ 3 = $1.40 each. 5-pack: $6.25 ÷ 5 = $1.25 each. Difference: $1.40 − $1.25 = $0.15.
Check yourself · Question 3
Leah has $10.00. Sticker sheets cost $1.35 each. She buys as many whole sheets as she can, with no tax. How much money is left?
Answer: B
10 ÷ 1.35 is about 7.4, so she can buy 7 sheets. 7 × $1.35 = $9.45, and 8 sheets would cost $10.80, too much. Left: $10.00 − $9.45 = $0.55.
Common mistake
"10 ÷ 1.35 is about 7.4, so she has 40 cents left."
- Why it's tempting
- The calculator shows .4 after the 7, and it looks like money.
- Do this instead
- The .4 means four-tenths of a sheet. Round down to 7 sheets, multiply back to get $9.45, then subtract from $10.00.
Step 5 of 6
What to remember
Remember
- Find the total cost before you find the change.
- For a missing price, start with payment − change, take out the known items, then divide.
- Compare packs by the price of one item, and round down when counting whole items a budget can buy.
Step 6 of 6
Practice on a real question
Use what you just learned on this question, then check the explanation.
Try another one
In your own words
In the practice question, what is the total cost before you subtract, and which wrong choice is that total?