Math review worksheet with arithmetic problems for practice.

Let’s solve each problem one by one. I’ll go step by step and check my work carefully.

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1. 67 × 31

Break it down:
67 × 30 = 2010
67 × 1 = 67
Add them: 2010 + 67 = 2077

✔ Check: 67 × 31 = (60+7)(30+1) = 60×30 + 60×1 + 7×30 + 7×1 = 1800 + 60 + 210 + 7 = 2077 ✔️

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2. 2,637 + 832

Align by place value:

```
2637
+ 832
------
```

7 + 2 = 9
3 + 3 = 6
6 + 8 = 14 → write 4, carry 1
2 + 0 + 1 = 3

→ 3,469

✔ Check: 2637 + 800 = 3437; 3437 + 32 = 3469 ✔️

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3. 48 - 19

48 - 10 = 38
38 - 9 = 29

✔ Or: 48 - 20 = 28, then +1 = 29 ✔️

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4. 928 - 45

928 - 40 = 888
888 - 5 = 883

✔ Check: 883 + 45 = 928 ✔️

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5. 21,306 - 3,714

Subtract:

```
21306
- 3714
-------
```

6 - 4 = 2
0 - 1 → borrow → 10 - 1 = 9 (but tens digit was 0, so need to borrow from hundreds)

Actually, let’s do it properly:

Start from right:

Units: 6 - 4 = 2
Tens: 0 - 1 → can’t, borrow from hundreds. But hundreds is 3 → becomes 2, tens become 10. Now 10 - 1 = 9? Wait — no:

Wait, original number: 21,306

Digits: Ten-thousands: 2, Thousands: 1, Hundreds: 3, Tens: 0, Units: 6

Minus: 3,714 → which is 0 ten-thousands, 3 thousands, 7 hundreds, 1 ten, 4 units.

So:

Units: 6 - 4 = 2
Tens: 0 - 1 → borrow from hundreds. Hundreds is 3 → becomes 2, tens become 10. 10 - 1 = 9
Hundreds: 2 (after borrow) - 7 → can’t, borrow from thousands. Thousands is 1 → becomes 0, hundreds become 12. 12 - 7 = 5
Thousands: 0 (after borrow) - 3 → can’t, borrow from ten-thousands. Ten-thousands is 2 → becomes 1, thousands become 10. 10 - 3 = 7
Ten-thousands: 1 - 0 = 1

Result: 17,592

✔ Check: 17592 + 3714 = ?

17592 + 3000 = 20592
20592 + 700 = 21292
21292 + 14 = 21306 ✔️

---

6. 21 × 9

20 × 9 = 180
1 × 9 = 9
Total: 189

✔ Check: 21 × 10 = 210 minus 21 = 189 ✔️

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7. 14 × 18

Use distributive property:

14 × 10 = 140
14 × 8 = 112
140 + 112 = 252

✔ Or: 14 × 18 = (10+4)(10+8) = 100 + 80 + 40 + 32 = 252 ✔️

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8. 627 × 5

600 × 5 = 3000
27 × 5 = 135
Total: 3000 + 135 = 3135

✔ Check: 627 × 10 = 6270 ÷ 2 = 3135 ✔️

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9. 7,147 × 7

Break it:

7000 × 7 = 49,000
100 × 7 = 700
40 × 7 = 280
7 × 7 = 49

Add: 49000 + 700 = 49700
49700 + 280 = 49980
49980 + 49 = 50,029

✔ Check: Let me verify with another way:

7147 × 7:

7 × 7 = 49 → write 9, carry 4
4 × 7 = 28 + 4 = 32 → write 2, carry 3
1 × 7 = 7 + 3 = 10 → write 0, carry 1
7 × 7 = 49 + 1 = 50 → write 50

So: 50,029 ✔️

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10. 87 × 54

Use multiplication:

First: 87 × 50 = 4350
Then: 87 × 4 = 348
Add: 4350 + 348 = 4698

✔ Check: 87 × 54 = (90-3)(50+4) = 90×50 + 90×4 -3×50 -3×4 = 4500 + 360 - 150 - 12 = 4860 - 162 = 4698 ✔️

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11. 627 × 33

627 × 30 = 18,810
627 × 3 = 1,881
Add: 18810 + 1881 = 20,691

✔ Check: 627 × 33 = 627 × (30 + 3) = same as above ✔️

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12. 283 × 724

This is big. Let’s break it:

We can do 283 × 700 = 198,100
283 × 20 = 5,660
283 × 4 = 1,132

Now add:

198100
+ 5660 = 203,760
+ 1132 = 204,892

✔ Let me verify with column multiplication mentally:

But since this is time-consuming, and we did breakdown correctly, I’ll trust it for now.

Alternatively, use calculator-style thinking: but since we’re doing manually, let’s accept 204,892.

Wait — actually, let me double-check:

283 × 724

Do 283 × 700 = 283 × 7 × 100 = 1981 × 100 = 198,100 ✔️
283 × 20 = 5,660 ✔️
283 × 4 = 1,132 ✔️

Sum: 198100 + 5660 = 203760
203760 + 1132 = 204892 ✔️

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13. 9 ) 81 → That means 81 ÷ 9 = 9

✔ Because 9 × 9 = 81

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14. 7 ) 53 → 53 ÷ 7

7 × 7 = 49
53 - 49 = 4 → so 7 R4 or as mixed number: 7 and 4/7

But looking at format, probably wants quotient and remainder.

In the image, it's written as "7 ) 53" meaning divide 53 by 7.

Answer: 7 remainder 4

But in some contexts, they might want decimal or fraction. Looking at other problems like #18, they have fractions, so maybe here too?

Wait, problem 18 is “21^4 =” — that seems odd. Probably typo? Maybe 21/4?

Looking back at user input:

“18. 21^4 =” — that doesn't make sense in context. Likely a formatting error. In many worksheets, “a ) b” means b ÷ a.

Similarly, 13. 9 ) 81 → 81 ÷ 9 = 9

14. 7 ) 53 → 53 ÷ 7 = 7 R4

But perhaps they want improper fraction or mixed number? Since later problems have fractions.

Actually, looking at problem 18: “21^4 =” — that must be a typo. Probably meant “21/4 =” because exponentiation doesn’t fit here.

Same with 19: “20/3 =”

And 20: “12/7 =”

So likely, 13 to 15 are division problems written as “divisor ) dividend”, and answers should be quotients with remainders or as mixed numbers.

But in standard math worksheet style, when written as “7 ) 53”, it often expects quotient and remainder.

However, given that problems 18–27 involve fractions, perhaps all divisions should be expressed as mixed numbers.

Let me check problem 15: “13 ) 156” → 156 ÷ 13 = 12 exactly.

Problem 16: “35 ) 702” → 702 ÷ 35

I think for consistency, since later problems ask for fractions, we should express these as mixed numbers where applicable.

But let’s see the pattern.

Actually, re-examining the original text:

"13. 9 ) 81" — this is likely 81 divided by 9.

Similarly, "14. 7 ) 53" — 53 divided by 7.

In elementary math, this notation usually means long division, and answer is quotient with remainder.

But to match the rest of the sheet, which has fractions, perhaps we should convert to mixed numbers.

Looking ahead:

18. 21^4 = — definitely a typo. Should be 21/4.

19. 20/3 =

20. 12/7 =

So yes, probably 13-15 are also meant to be fractions or mixed numbers.

For 13: 81 ÷ 9 = 9 → just 9

14: 53 ÷ 7 = 7 and 4/7 → 7 4/7

15: 156 ÷ 13 = 12 → 12

But let’s confirm 156 ÷ 13: 13×12=156 ✔️

So:

13. 9

14. 7 4/7 or 53/7? But since others are mixed, probably mixed.

In problem 20: “12/7 =” which is 1 5/7, so they expect simplified mixed numbers.

Similarly, 19: 20/3 = 6 2/3

So for 14: 53/7 = 7 4/7

But the notation “7 ) 53” might imply integer division. However, given the context, I’ll go with mixed numbers for consistency.

To be safe, let’s look at problem 16: “35 ) 702” → 702 ÷ 35

35 × 20 = 700, so 702 ÷ 35 = 20 and 2/35 → 20 2/35

Similarly, 17: “43 ) 824” → 824 ÷ 43

43 × 19 = 817, 824 - 817 = 7 → 19 7/43

So yes, all should be mixed numbers.

Therefore:

13. 81 ÷ 9 = 9 (which is 9/1, but just 9)

14. 53 ÷ 7 = 7 4/7

15. 156 ÷ 13 = 12

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16. 35 ) 702 → 702 ÷ 35

As above: 35 × 20 = 700, remainder 2 → 20 2/35

Can simplify? 2 and 35 coprime, so yes.

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17. 43 ) 824 → 824 ÷ 43

43 × 19 = let's compute: 40×19=760, 3×19=57, total 817

824 - 817 = 7 → 19 7/43

7 and 43 coprime.

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18. 21/4 = → 21 ÷ 4 = 5 with remainder 1 → 5 1/4

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19. 20/3 = → 20 ÷ 3 = 6 with remainder 2 → 6 2/3

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20. 12/7 = → 12 ÷ 7 = 1 with remainder 5 → 1 5/7

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21. 26/5 = → 26 ÷ 5 = 5 with remainder 1 → 5 1/5

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22. 1/7 + 5/7 = → same denominator, add numerators: (1+5)/7 = 6/7

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23. 3 2/5 - 1 4/5 =

First, convert to improper fractions or subtract directly.

3 2/5 = 17/5
1 4/5 = 9/5
17/5 - 9/5 = 8/5 = 1 3/5

Or directly: 3 - 1 = 2, but 2/5 - 4/5 can't, so borrow 1 from 3 → 2 + 5/5 + 2/5 = 2 7/5? No.

Better: 3 2/5 = 2 + 1 + 2/5 = 2 + 7/5? Messy.

Standard way: since 2/5 < 4/5, borrow 1 from whole number.

3 2/5 = 2 + (5/5 + 2/5) = 2 7/5

Now subtract 1 4/5: (2 - 1) + (7/5 - 4/5) = 1 + 3/5 = 1 3/5

✔

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24. 7/8 - 2/5 =

Find common denominator. LCM of 8 and 5 is 40.

7/8 = 35/40
2/5 = 16/40
35/40 - 16/40 = 19/40

19/40 is already simplified.

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25. 7 - 2/5 =

7 = 35/5
35/5 - 2/5 = 33/5 = 6 3/5

Or: 7 - 0.4 = 6.6, but better as fraction.

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26. 3 4/5 - 1 2/5 =

Whole numbers: 3 - 1 = 2
Fractions: 4/5 - 2/5 = 2/5
So 2 2/5

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27. 3 4/5 - 3 1/5 =

Whole numbers: 3 - 3 = 0
Fractions: 4/5 - 1/5 = 3/5
So 3/5

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Now, compiling all answers:

1. 2077
2. 3469
3. 29
4. 883
5. 17592
6. 189
7. 252
8. 3135
9. 50029
10. 4698
11. 20691
12. 204892
13. 9
14. 7 4/7
15. 12
16. 20 2/35
17. 19 7/43
18. 5 1/4
19. 6 2/3
20. 1 5/7
21. 5 1/5
22. 6/7
23. 1 3/5
24. 19/40
25. 6 3/5
26. 2 2/5
27. 3/5

I think that's all.

Final Answer:
1. 2077
2. 3469
3. 29
4. 883
5. 17592
6. 189
7. 252
8. 3135
9. 50029
10. 4698
11. 20691
12. 204892
13. 9
14. 7 \frac{4}{7}
15. 12
16. 20 \frac{2}{35}
17. 19 \frac{7}{43}
18. 5 \frac{1}{4}
19. 6 \frac{2}{3}
20. 1 \frac{5}{7}
21. 5 \frac{1}{5}
22. \frac{6}{7}
23. 1 \frac{3}{5}
24. \frac{19}{40}
25. 6 \frac{3}{5}
26. 2 \frac{2}{5}
27. \frac{3}{5}