Mental Math: Subtraction Strategies

Show your work for each problem.

1.
The numbers in $63 - 58$ are close together. Which strategy from this lesson fits best?
1. a)Standard written algorithm
2. b)Counting up (since 58 and 63 are close together)
3. c)Compensation (round 58 to 60)
4. d)Breaking apart by place value
Answer: Counting up (since 58 and 63 are close together)
Counting up is ideal when numbers are close: $58 + 2 = 60$ , $60 + 3 = 63$ . Total: $2 + 3 = 5$ . Quick and simple!
2.
Calculate $50 - 23$ using the counting up strategy. What is the answer?
Answer: 27
Count up: $23 + 7 = 30$ , then $30 + 20 = 50$ . Total: $7 + 20 = 27$ . So $50 - 23 = 27$ .
3.
Use compensation to calculate $74 - 29$ . What is the answer?
Answer: 45
$74 - 30 = 44$ . Since 30 is 1 more than 29, add 1 back: $44 + 1 = 45$ .
4.
Calculate $86 - 43$ using the breaking apart strategy.
Answer: 43
1. Break apart 43 into tens and ones: $43 = ?$ 40 + 3
2. Subtract the tens: $86 - 40 = ?$ 46
3. Subtract the ones: $46 - 3 = ?$ 43
5.
When using compensation for $65 - 28$ , you first calculate $65 - 30 = 35$ . What do you do next?
1. a)Subtract 2 to get 33
2. b)The answer is already 35
3. c)Add 30 to get 65
4. d)Add 2 to get 37
Answer: Add 2 to get 37
Since 30 is 2 more than 28, you subtracted 2 too many. Add 2 back: $35 + 2 = 37$ .
6.
Calculate $100 - 47$ using the complement strategy (9 minus tens, 10 minus ones).
Answer: 53
Tens: $9 - 4 = 5$ . Ones: $10 - 7 = 3$ . Together: $53$ . Check: $47 + 53 = 100$ ✓
7.
Calculate $92 - 47$ using the counting up strategy.
Answer: 45
1. Start at 47. Jump to the next ten: $47 + ? = 50$ 3
2. From 50, jump to 90: $50 + ? = 90$ 40
3. From 90, jump to 92: $90 + ? = 92$ 2
4. Add all jumps: $3 + 40 + 2 = ?$ 45
8.
A book costs 38 dollars. You pay with a 50 dollar bill. Using mental math, how much change should you receive?
1. a)22 dollars
2. b)18 dollars
3. c)8 dollars
4. d)12 dollars
Answer: 12 dollars
Using compensation: $50 - 40 = 10$ . Since 38 is 2 less than 40, add 2: $10 + 2 = 12$ dollars.
9.
Calculate $100 - 72$ mentally.
Answer: 28
$9 - 7 = 2$ (tens), $10 - 2 = 8$ (ones). Answer: $28$ . Check: $72 + 28 = 100$ ✓
10.
Calculate $83 - 49$ using the compensation strategy.
Answer: 34
1. Round 49 to the nearest ten: $49 \approx ?$ 50
2. Subtract the rounded number: $83 - 50 = ?$ 33
3. Did you subtract too much or too little? By how much? 1
4. Adjust: $33 + 1 = ?$ 34
11.
Your team scored 91 points. The opponent scored 67 points. What is the point difference?
Answer: 24
Using compensation: $91 - 70 = 21$ . Since 70 is 3 more than 67, add 3: $21 + 3 = 24$ points.
12.
A movie is 95 minutes long. You've watched 58 minutes. How many minutes are left?
Answer: 37
1. Use compensation: round 58 to the nearest ten. What number do you get? 60
2. Calculate $95 - 60 = ?$ 35
3. You rounded 58 up by 2. Should you add or subtract 2? add
4. Final answer: $35 + 2 = ?$ 37
13.
Which calculation shows the correct use of compensation for $72 - 38$ ?
1. a) $70 - 40 = 30$ , then $30 + 2 = 32$
2. b) $72 - 40 = 32$ , then $32 - 2 = 30$
3. c) $72 - 40 = 32$ , then $32 + 2 = 34$
4. d) $72 - 38 = 32$ , then $32 + 2 = 34$
Answer: $72 - 40 = 32$ , then $32 + 2 = 34$
Round 38 to 40. Calculate $72 - 40 = 32$ . Since 40 is 2 more than 38, you subtracted 2 too many. Add 2 back: $32 + 2 = 34$ .
14.
Calculate $100 - 84$ using any mental math strategy.
Answer: 16
Using the complement to 100: $9 - 8 = 1$ (tens), $10 - 4 = 6$ (ones). Answer: $16$ . Check: $84 + 16 = 100$ ✓
15.
You have 75 dollars. After buying a gift for 48 dollars, how much money do you have left?
Answer: 27
1. Use compensation: round 48 to the nearest ten. What number do you get? 50
2. Subtract the rounded amount: $75 - 50 = ?$ 25
3. How much did you round up by? $50 - 48 = ?$ 2
4. Adjust by adding back: $25 + 2 = ?$ 27