Mental Math Strategies worksheet with examples and exercises for adding and subtracting using breaking apart and compensation techniques.
Mental math strategies worksheet showing examples of adding and subtracting by breaking apart numbers and using compensation, with practice problems for students.
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Step-by-step solution for: Mental Math Strategies Worksheet | Mental maths worksheets, Mental ...
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Show Answer Key & Explanations
Step-by-step solution for: Mental Math Strategies Worksheet | Mental maths worksheets, Mental ...
Let’s solve each problem step by step using the mental math strategies shown: breaking apart numbers and compensation.
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Section 1: Add or subtract mentally. Use breaking apart.
We break numbers into tens and ones (or hundreds, tens, ones) to make adding/subtracting easier.
1. 39 + 28
Break 39 → 30 + 9
Break 28 → 20 + 8
Add tens: 30 + 20 = 50
Add ones: 9 + 8 = 17
Total: 50 + 17 = 67
2. 47 + 39
Break 47 → 40 + 7
Break 39 → 30 + 9
Tens: 40 + 30 = 70
Ones: 7 + 9 = 16
Total: 70 + 16 = 86
3. 69 – 32
Break 69 → 60 + 9
Break 32 → 30 + 2
Subtract tens: 60 – 30 = 30
Subtract ones: 9 – 2 = 7
Total: 30 + 7 = 37
4. 349 – 218
Break 349 → 300 + 40 + 9
Break 218 → 200 + 10 + 8
Hundreds: 300 – 200 = 100
Tens: 40 – 10 = 30
Ones: 9 – 8 = 1
Total: 100 + 30 + 1 = 131
5. 832 – 411
Break 832 → 800 + 30 + 2
Break 411 → 400 + 10 + 1
Hundreds: 800 – 400 = 400
Tens: 30 – 10 = 20
Ones: 2 – 1 = 1
Total: 400 + 20 + 1 = 421
6. 849 + 130
Break 849 → 800 + 40 + 9
Break 130 → 100 + 30 + 0
Hundreds: 800 + 100 = 900
Tens: 40 + 30 = 70
Ones: 9 + 0 = 9
Total: 900 + 70 + 9 = 979
7. 362 – 105
Break 362 → 300 + 60 + 2
Break 105 → 100 + 0 + 5
Hundreds: 300 – 100 = 200
Tens: 60 – 0 = 60
Ones: 2 – 5 → can’t do! So we need to adjust — but since this is “breaking apart”, let’s think differently:
Actually, 362 – 105 = (362 – 100) – 5 = 262 – 5 = 257
But if we must break both:
362 = 300 + 60 + 2
105 = 100 + 0 + 5
So: (300 – 100) + (60 – 0) + (2 – 5) → 200 + 60 + (-3) = 257 ✔
8. 486 + 362
Break 486 → 400 + 80 + 6
Break 362 → 300 + 60 + 2
Hundreds: 400 + 300 = 700
Tens: 80 + 60 = 140
Ones: 6 + 2 = 8
Now add: 700 + 140 = 840; 840 + 8 = 848
9. 314 + 129
Break 314 → 300 + 10 + 4
Break 129 → 100 + 20 + 9
Hundreds: 300 + 100 = 400
Tens: 10 + 20 = 30
Ones: 4 + 9 = 13
Total: 400 + 30 + 13 = 443
10. 437 + 210
Break 437 → 400 + 30 + 7
Break 210 → 200 + 10 + 0
Hundreds: 400 + 200 = 600
Tens: 30 + 10 = 40
Ones: 7 + 0 = 7
Total: 600 + 40 + 7 = 647
11. 739 – 420
Break 739 → 700 + 30 + 9
Break 420 → 400 + 20 + 0
Hundreds: 700 – 400 = 300
Tens: 30 – 20 = 10
Ones: 9 – 0 = 9
Total: 300 + 10 + 9 = 319
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Section 2: Add or subtract mentally. Use compensation.
Compensation means adjusting one number to make it easier (like making a round number), then fixing the answer at the end.
12. 49 + 26
Make 49 into 50 by adding 1.
So: 50 + 26 = 76
But we added 1 extra, so subtract 1: 76 – 1 = 75
13. 58 – 23
Make 23 into 20 by subtracting 3.
So: 58 – 20 = 38
But we subtracted 3 less than we should have, so subtract 3 more: 38 – 3 = 35
Wait — actually, compensation for subtraction:
If you subtract less, you get a bigger result, so you need to subtract the difference.
Better way:
To make 23 into 25? Or 20? Let’s try making 58 into 60.
Alternative: Make 58 into 60 (+2). Then 60 – 23 = 37. But we added 2 to 58, so our answer is too big by 2 → 37 – 2 = 35
Same answer.
Or: Make 23 into 20 (subtract 3 from subtrahend). Then 58 – 20 = 38. Since we made the subtrahend smaller by 3, the result is 3 too big → 38 – 3 = 35
✔
14. 78 + 40
This is easy already. 78 + 40 = 118. No compensation needed. But if we want:
Make 78 into 80 (+2). 80 + 40 = 120. Subtract 2 → 118. Same.
Answer: 118
15. 90 – 29
Make 29 into 30 (+1).
90 – 30 = 60
But we subtracted 1 too many, so add 1 back: 60 + 1 = 61
16. 439 + 396
Make 396 into 400 (+4).
439 + 400 = 839
But we added 4 extra, so subtract 4: 839 – 4 = 835
17. 825 – 299
Make 299 into 300 (+1).
825 – 300 = 525
But we subtracted 1 too many, so add 1 back: 525 + 1 = 526
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Final Answer:
1. 67
2. 86
3. 37
4. 131
5. 421
6. 979
7. 257
8. 848
9. 443
10. 647
11. 319
12. 75
13. 35
14. 118
15. 61
16. 835
17. 526
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Section 1: Add or subtract mentally. Use breaking apart.
We break numbers into tens and ones (or hundreds, tens, ones) to make adding/subtracting easier.
1. 39 + 28
Break 39 → 30 + 9
Break 28 → 20 + 8
Add tens: 30 + 20 = 50
Add ones: 9 + 8 = 17
Total: 50 + 17 = 67
2. 47 + 39
Break 47 → 40 + 7
Break 39 → 30 + 9
Tens: 40 + 30 = 70
Ones: 7 + 9 = 16
Total: 70 + 16 = 86
3. 69 – 32
Break 69 → 60 + 9
Break 32 → 30 + 2
Subtract tens: 60 – 30 = 30
Subtract ones: 9 – 2 = 7
Total: 30 + 7 = 37
4. 349 – 218
Break 349 → 300 + 40 + 9
Break 218 → 200 + 10 + 8
Hundreds: 300 – 200 = 100
Tens: 40 – 10 = 30
Ones: 9 – 8 = 1
Total: 100 + 30 + 1 = 131
5. 832 – 411
Break 832 → 800 + 30 + 2
Break 411 → 400 + 10 + 1
Hundreds: 800 – 400 = 400
Tens: 30 – 10 = 20
Ones: 2 – 1 = 1
Total: 400 + 20 + 1 = 421
6. 849 + 130
Break 849 → 800 + 40 + 9
Break 130 → 100 + 30 + 0
Hundreds: 800 + 100 = 900
Tens: 40 + 30 = 70
Ones: 9 + 0 = 9
Total: 900 + 70 + 9 = 979
7. 362 – 105
Break 362 → 300 + 60 + 2
Break 105 → 100 + 0 + 5
Hundreds: 300 – 100 = 200
Tens: 60 – 0 = 60
Ones: 2 – 5 → can’t do! So we need to adjust — but since this is “breaking apart”, let’s think differently:
Actually, 362 – 105 = (362 – 100) – 5 = 262 – 5 = 257
But if we must break both:
362 = 300 + 60 + 2
105 = 100 + 0 + 5
So: (300 – 100) + (60 – 0) + (2 – 5) → 200 + 60 + (-3) = 257 ✔
8. 486 + 362
Break 486 → 400 + 80 + 6
Break 362 → 300 + 60 + 2
Hundreds: 400 + 300 = 700
Tens: 80 + 60 = 140
Ones: 6 + 2 = 8
Now add: 700 + 140 = 840; 840 + 8 = 848
9. 314 + 129
Break 314 → 300 + 10 + 4
Break 129 → 100 + 20 + 9
Hundreds: 300 + 100 = 400
Tens: 10 + 20 = 30
Ones: 4 + 9 = 13
Total: 400 + 30 + 13 = 443
10. 437 + 210
Break 437 → 400 + 30 + 7
Break 210 → 200 + 10 + 0
Hundreds: 400 + 200 = 600
Tens: 30 + 10 = 40
Ones: 7 + 0 = 7
Total: 600 + 40 + 7 = 647
11. 739 – 420
Break 739 → 700 + 30 + 9
Break 420 → 400 + 20 + 0
Hundreds: 700 – 400 = 300
Tens: 30 – 20 = 10
Ones: 9 – 0 = 9
Total: 300 + 10 + 9 = 319
---
Section 2: Add or subtract mentally. Use compensation.
Compensation means adjusting one number to make it easier (like making a round number), then fixing the answer at the end.
12. 49 + 26
Make 49 into 50 by adding 1.
So: 50 + 26 = 76
But we added 1 extra, so subtract 1: 76 – 1 = 75
13. 58 – 23
Make 23 into 20 by subtracting 3.
So: 58 – 20 = 38
But we subtracted 3 less than we should have, so subtract 3 more: 38 – 3 = 35
Wait — actually, compensation for subtraction:
If you subtract less, you get a bigger result, so you need to subtract the difference.
Better way:
To make 23 into 25? Or 20? Let’s try making 58 into 60.
Alternative: Make 58 into 60 (+2). Then 60 – 23 = 37. But we added 2 to 58, so our answer is too big by 2 → 37 – 2 = 35
Same answer.
Or: Make 23 into 20 (subtract 3 from subtrahend). Then 58 – 20 = 38. Since we made the subtrahend smaller by 3, the result is 3 too big → 38 – 3 = 35
✔
14. 78 + 40
This is easy already. 78 + 40 = 118. No compensation needed. But if we want:
Make 78 into 80 (+2). 80 + 40 = 120. Subtract 2 → 118. Same.
Answer: 118
15. 90 – 29
Make 29 into 30 (+1).
90 – 30 = 60
But we subtracted 1 too many, so add 1 back: 60 + 1 = 61
16. 439 + 396
Make 396 into 400 (+4).
439 + 400 = 839
But we added 4 extra, so subtract 4: 839 – 4 = 835
17. 825 – 299
Make 299 into 300 (+1).
825 – 300 = 525
But we subtracted 1 too many, so add 1 back: 525 + 1 = 526
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Final Answer:
1. 67
2. 86
3. 37
4. 131
5. 421
6. 979
7. 257
8. 848
9. 443
10. 647
11. 319
12. 75
13. 35
14. 118
15. 61
16. 835
17. 526
Parent Tip: Review the logic above to help your child master the concept of math worksheet mental addition subtraction.
