Singapore Math and Mixed Work worksheet with arithmetic problems and number puzzles.

Let’s solve each problem step by step.

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Top Left Section:

1. 71 - 44 = ?
71 minus 40 is 31, then minus 4 more → 27
✔ Answer: 27

2. 882 - 789 = ?
882 - 700 = 182
182 - 89 = ?
182 - 80 = 102; 102 - 9 = 93
✔ Answer: 93

3. 422 + 166 = ?
400 + 100 = 500
22 + 66 = 88
Total: 500 + 88 = 588
✔ Answer: 588

4. 4 + 7 + 6 = ?
4 + 7 = 11; 11 + 6 = 17
✔ Answer: 17

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Fractions (top middle):

We are adding fractions with same denominators — just add numerators.

- 6/9 + 2/9 = (6+2)/9 = 8/9
- 3/5 + 1/5 = (3+1)/5 = 4/5
- 3/7 + 2/7 = (3+2)/7 = 5/7

✔ Answers: 8/9, 4/5, 5/7

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Addition Squares (middle right):

First square: Use numbers 10, 16, 17, 29, 21, 36, 50, and 59

Given:
Row sums: 89, 114, 102
Column sums: 101, 46, 132, 111? Wait — actually looking at layout:

It's a 3x3 grid. Row totals on right: 89, 114, 102
Column totals on bottom: 101, 46, 132? But there are 4 column totals listed? That doesn’t match.

Wait — let me re-read the instruction:

> “Use these numbers: 10, 16, 17, 29, 21, 36, 50, and 59” — that’s 8 numbers. Plus one given: 42 in top-left. So total 9 cells.

Grid has row sums: 89, 114, 102
Column sums: 101, 46, 132? But 101 + 46 + 132 = 279
Row sums: 89 + 114 + 102 = 305 → mismatch.

Wait — maybe I misread. Let me check again.

Actually, looking at the image description (even though we don’t describe it), the user provided text says:

“Fill in the missing numbers to complete the addition square.”

And for first square:

Numbers to use: 10, 16, 17, 29, 21, 36, 50, 59
Plus 42 already placed.

So 9 numbers total.

Row sums: 89, 114, 102 → sum = 305
Column sums: 101, 46, 132? But 101+46+132=279 — not matching.

Wait — perhaps the column sums are written below as: 101, 46, 132, 111? That can’t be — 3 columns should have 3 sums.

Looking back at original text:

In the image transcription, under first square:

Row sums: 89, 114, 102
Below grid: 101, 46, 132, 111 — that’s four numbers? That must be a typo or misalignment.

Wait — perhaps it’s:

The grid is 3x3.

Row 1 sum: 89 → cell1=42, so cell2 + cell3 = 89 - 42 = 47
Row 2 sum: 114
Row 3 sum: 102

Column 1 sum: 101 → cell1=42, so cell4 + cell7 = 101 - 42 = 59
Column 2 sum: 46
Column 3 sum: 132? But 132 seems too big.

Wait — let’s list all available numbers: 10,16,17,29,21,36,50,59 plus 42.

Total sum of all 9 numbers:
42 + 10+16+17+29+21+36+50+59 =
42 + (10+59)=69; (16+50)=66; (17+36)=53; (29+21)=50 → 69+66=135; +53=188; +50=238; +42=280? Wait no — 42 is included separately.

Better:
List: 10,16,17,21,29,36,42,50,59
Sum:
10+59=69
16+50=66
17+42=59
21+36=57
29 left → wait, 9 numbers.

Group:
(10+59) = 69
(16+50) = 66
(17+42) = 59
(21+36) = 57
29 → total = 69+66=135; +59=194; +57=251; +29=280

Now row sums: 89+114+102 = 305 → not 280 → contradiction.

Wait — perhaps the row sums include something else? Or maybe I miscounted.

Alternative approach: Maybe the "row sums" are not the full row but partial? Unlikely.

Perhaps the numbers to use are only the 8 listed, and 42 is extra? But 8 numbers for 8 empty cells? Grid has 9 cells, one filled.

I think there might be an error in my interpretation.

Let me try solving logically.

Assume grid:

A B C | 89
D E F | 114
G H I | 102
------
101 46 132? ← but 101+46+132=279 ≠ 305

Unless the last number 111 is for something else.

Looking back at user input:

Under first square:
"101 46 132 111" — perhaps it's two sets? No.

Another idea: maybe the column sums are 101, 46, and 132 is wrong — or perhaps 132 is for diagonal? Unlikely.

Wait — let's calculate what the column sums should be if row sums are 89,114,102 → total 305, so column sums must also sum to 305.

If column1=101, column2=46, then column3 must be 305 - 101 - 46 = 158.

But 158 is not among the numbers listed below. The numbers listed are 101,46,132,111 — none is 158.

This suggests a possible typo in the problem or in my reading.

Perhaps "132" is "158"? Or "111" is part of another section.

Let me look at the second square for clue.

Second square: Use numbers 15,18,22,28,43,46,82

Given: 79 in top-right, 21 in bottom-left, 16 in bottom-middle.

Row sums: 82, 79, 103? Wait, from text:

"82
79
103" — probably row sums.

Column sums: 89,83,72,105 — again four numbers.

This is confusing.

Perhaps the numbers below the grid are not all column sums — maybe some are for diagonals or other.

To save time and since this is for a student, let's assume standard magic square logic where rows, columns, and sometimes diagonals sum to same value, but here they give different sums.

Another approach: for the first square, with 42 in top-left, and row1 sum 89, so B+C = 47.

Available numbers: 10,16,17,21,29,36,50,59

Which two add to 47? 10+37 no, 16+31 no, 17+30 no, 21+26 no, 29+18 no, 36+11 no, 50-3 no, 59-12 no — none add to 47.

10+37 not available, 16+31 not, etc. 29+18 not available.

What about 10+37? 37 not in list. 17+30 no. Perhaps 50-3, no.

Wait, 10+37 not, but 16+31 not, 17+30 not, 21+26 not, 29+18 not, 36+11 not, 50+ (-3) no.

None of the pairs from the list add to 47.

10+37 — 37 not available. 16+31 — 31 not. 17+30 — 30 not. 21+26 — 26 not. 29+18 — 18 not. 36+11 — 11 not. 50+ (-3) no. 59+ (-12) no.

So impossible? That can't be.

Unless I missed a pair. What about 10 and 37? No. 16 and 31? No. Perhaps 29 and 18, but 18 not in list.

List is: 10,16,17,21,29,36,50,59

Try 10+37 — no. 16+31 — no. 17+30 — no. 21+26 — no. 29+18 — no. 36+11 — no. 50+ (-3) — no. 59+ (-12) — no.

No two numbers from the list add to 47. So either the problem has a mistake, or I have a mistake.

Perhaps the row sum is not 89 for the first row? Or perhaps 42 is not in the first cell.

Another idea: perhaps "42" is not in the grid, but that doesn't make sense.

Or perhaps the numbers to use include 42, but 42 is already used, so the 8 numbers are for the remaining 8 cells.

But still, B+C=47, and no two from {10,16,17,21,29,36,50,59} add to 47.

Let's calculate all possible pairs:

10+16=26
10+17=27
10+21=31
10+29=39
10+36=46
10+50=60
10+59=69
16+17=33
16+21=37
16+29=45
16+36=52
16+50=66
16+59=75
17+21=38
17+29=46
17+36=53
17+50=67
17+59=76
21+29=50
21+36=57
21+50=71
21+59=80
29+36=65
29+50=79
29+59=88
36+50=86
36+59=95
50+59=109

None is 47. Closest are 46 (10+36 or 17+29).

So perhaps the row sum is 88? But it's given as 89.

Maybe it's 42 + B + C = 89, so B+C=47, but no pair makes 47, so perhaps the problem has a typo, or I need to use a number twice, but that's unlikely.

For the sake of progressing, let's assume that for the first square, we can skip or guess, but that's not good.

Perhaps "89" is for the column, not row. Let's try that.

Suppose the 89 is the sum of the first column: A+D+G = 89, and A=42, so D+G=47.

Then from the list, which two add to 47? Still no pair.

Same issue.

Perhaps the numbers are to be used, but not necessarily all, but the instruction says "use these numbers", implying all.

Another thought: perhaps "101 46 132 111" are not column sums, but something else. For example, in some puzzles, they give the sum of diagonals or other.

But typically in addition squares, it's rows and columns.

Let's look at the second square for insight.

Second square: use 15,18,22,28,43,46,82

Given: 79 in top-right, 21 in bottom-left, 16 in bottom-middle.

So grid:

A B 79 | say R1
C D E | R2
21 16 F | R3
Col sums: S1,S2,S3

From text, row sums are given as 82,79,103? In the user input: "82\n79\n103" likely row sums.

Column sums: "89 83 72 105" — again four numbers.

Perhaps the last number is for the diagonal or total.

Assume row sums: R1=82, R2=79, R3=103

Then A+B+79 = 82 → A+B = 3
C+D+E = 79
21+16+F = 103 → 37+F=103 → F=66

But 66 is not in the list of numbers to use: 15,18,22,28,43,46,82 — no 66.

So F=66 not available. Contradiction.

If R3=103, and 21+16=37, so F=66, but 66 not in list, so perhaps R3 is not 103.

In the user input, for second square, it says:

"82
79
103" — but perhaps 103 is not a row sum.

Maybe it's the sum of the last row or something else.

Perhaps the numbers "82,79,103" are the row sums, but for the second square, the given numbers are 79,21,16, and to use 15,18,22,28,43,46,82.

So let's denote the grid as:

P Q 79
R S T
21 16 U

Row1 sum: P+Q+79 = ? If 82, then P+Q=3, impossible with positive integers from the list.

If the 82 is for column1, then P+R+21 = 82 → P+R=61

Similarly, if 79 is for column2, Q+S+16 = 79 → Q+S=63

If 103 is for column3, 79+T+U = 103 → T+U=24

Then row sums are not given, or vice versa.

But in the text, it's listed as "82\n79\n103" after the grid, likely row sums.

Perhaps for the second square, the row sums are 82,79,103, but with 79 in top-right, so for row1: P+Q+79 = 82 → P+Q=3, which is impossible since smallest numbers are 15,18, etc.

So likely, the 82,79,103 are not row sums for the second square.

Perhaps they are the column sums.

Let me assume for second square:

Column1 sum: 82 → P+R+21 = 82 → P+R=61
Column2 sum: 79 → Q+S+16 = 79 → Q+S=63
Column3 sum: 103 → 79+T+U = 103 → T+U=24

Then the numbers to use are 15,18,22,28,43,46,82 for P,Q,R,S,T,U (6 cells), and 79,21,16 are given, so total 9 cells.

Numbers available: 15,18,22,28,43,46,82

P+R=61, possible pairs from list: 15+46=61, 18+43=61, 22+39 no, 28+33 no, etc. So possible: (15,46) or (18,43) or (43,18) or (46,15)

Q+S=63: possible pairs: 15+48 no, 18+45 no, 22+41 no, 28+35 no, 43+20 no, 46+17 no, 82-19 no. 15+48 not, 18+45 not, 22+41 not, 28+35 not, 43+20 not, 46+17 not, 82+ (-19) no. No pair adds to 63.

15+48 not available, 18+45 not, 22+41 not, 28+35 not, 43+20 not, 46+17 not, 82+ (-19) no.

Closest: 46+17=63, but 17 not in list. 43+20=63, 20 not. 28+35=63, 35 not. So no pair for 63.

T+U=24: possible pairs: 15+9 no, 18+6 no, 22+2 no, 28-4 no, etc. From list: 15+9 not, 18+6 not, 22+2 not, 28-4 not, 43-19 not, etc. 15+9 not available. Smallest sum is 15+18=33 >24, so impossible.

So this is not working.

Perhaps the "82,79,103" are the row sums, but for the second square, the given 79 is not in the grid for row1, but that doesn't make sense.

Another idea: perhaps "79" in the grid is the sum, not a cell value. But the instruction says "fill in the missing numbers", and "use these numbers", so likely the numbers in the grid are to be filled with the given set.

For the second square, it says "79" in the top-right cell, "21" in bottom-left, "16" in bottom-middle, so those are fixed values, not sums.

Then with row sums 82,79,103, we have conflict as above.

Perhaps the row sums are for the rows, but 82 for row1: P+Q+79 = 82 → P+Q=3, impossible.

Unless the 79 is not in the cell, but that contradicts the description.

Perhaps "79" is the sum of the first row, and the cell is blank, but the user said "79" is in the grid.

I think there might be a mistake in the problem or in my understanding.

To move forward, let's focus on the parts that are clear.

For the first few problems, we have answers.

For the addition squares, perhaps we can skip or assume, but that's not good.

Let's try the first square with a different assumption.

Suppose for the first square, the row sums are 89, 114, 102, and column sums are 101, 46, and let's calculate what the third column sum should be: total sum of all cells is sum of row sums = 89+114+102 = 305.

Sum of column1 and column2: 101+46 = 147, so column3 = 305-147 = 158.

But 158 is not in the list, and the list has 132,111, etc.

Perhaps the "132" is "158" typo.

Or perhaps "111" is for something else.

Another idea: perhaps the numbers "101,46,132,111" are the sums for the rows and columns combined, but that doesn't help.

Let's calculate the sum of the given numbers for the first square: 10,16,17,21,29,36,50,59,42 = as before, 280.

But row sums sum to 305, so discrepancy of 25, which is large.

Perhaps the 42 is not to be added, but that doesn't make sense.

I recall that in some addition squares, the sum of the row sums equals the sum of the column sums, and both equal the sum of all cells.

Here, if sum of cells is S, then sum of row sums = S, sum of column sums = S.

For first square, if row sums are 89,114,102, sum=305, so S=305.

But sum of given numbers is 280, so missing 25, which is not possible.

Unless the numbers to use are different.

Perhaps "use these numbers" means select from them, not use all, but the instruction implies use all.

For the sake of completing, let's assume that for the first square, we can find a combination.

Suppose we ignore the column sums for now.

Grid:

42 A B | 89
C D E | 114
F G H | 102
Col sums: 101,46,158 (assumed)

From row1: 42+A+B=89 → A+B=47

From col1: 42+C+F=101 → C+F=59

From col2: A+D+G=46

From col3: B+E+H=158

From row2: C+D+E=114

From row3: F+G+H=102

Also, the numbers to use: 10,16,17,21,29,36,50,59 for A,B,C,D,E,F,G,H

A+B=47, and from earlier, no two from the list add to 47, so perhaps A and B are not both from the list, but that can't be.

Unless 42 is not fixed, but it is given.

Perhaps "42" is the sum, not a cell value. But the user said "42" is in the grid.

I think there might be an error in the problem, or in the transcription.

Perhaps for the first square, the "42" is in a different position.

Another idea: perhaps the grid is:

| | | 89
| | | 114
| | | 102
101 46 132 111

But that doesn't help.

Perhaps the 111 is the sum of the diagonal or something.

Let's try to use the numbers.

Suppose for row1: 42 + x + y = 89, so x+y=47.

From the list, closest are 10+36=46, 17+29=46, 16+31 not, etc. So perhaps it's 46, and the row sum is 88, but it's given as 89.

Maybe it's 42 + 10 + 37, but 37 not available.

I think for the purpose of this response, since the other parts are solvable, and this part may have a typo, I'll provide the answers for the clear parts, and for the squares, I'll do my best.

Let's look at the bottom section: simple additions.

"4 + _ = 6" → 2
"9 + _ = 12" → 3
"5 + _ = 10" → 5
"7 + _ = 11" → 4

Easy.

Now for the vertical additions on the right:

3,963 + 6,867 = ?
3963 + 6867 = let's calculate:
3000+6000=9000
963+867=1830
Total 9000+1830=10830
✔ 10,830

2,151 + 2,980 = 2151+2980 = 5131
✔ 5,131

8,868 - 8,472 = 8868-8472 = 396
✔ 396

8,817 - 1,283 = 8817-1283 = 7534
✔ 7,534

99,999 - 91,113 = 99999-91113 = 8886
✔ 8,886

95,989 - 70,121 = 95989-70121 = 25868
✔ 25,868

Ω + Π = ? — this is symbolic, probably not to be solved, or perhaps it's a trick, but likely it's just to leave as is, or perhaps it's 0, but no context. Probably not required, or perhaps it's a placeholder.

In the context, it might be that Ω and Π are variables, but no values given, so perhaps omit or say unknown.

But in the image, it might be that it's to be left blank, or perhaps it's a joke.

For now, I'll skip or put "unknown".

But let's see the whole thing.

Perhaps for the addition squares, we can solve the second one.

Second square: use 15,18,22,28,43,46,82

Given: 79 in top-right, 21 in bottom-left, 16 in bottom-middle.

Assume row sums are 82,79,103 as given.

Then for row3: 21 + 16 + U = 103 → 37 + U = 103 → U = 66, but 66 not in list, so impossible.

If the 103 is not for row3, perhaps it's for column3.

Assume column sums are 82,79,103.

Then col1: P + R + 21 = 82 → P+R=61
Col2: Q + S + 16 = 79 → Q+S=63
Col3: 79 + T + U = 103 → T+U=24

Numbers for P,Q,R,S,T,U: 15,18,22,28,43,46,82 — 7 numbers, but only 6 cells, so perhaps one is not used, or 79,21,16 are not from the list, which they aren't.

The list is for the missing cells, so 6 cells to fill with 7 numbers? That doesn't make sense.

The instruction says "use these numbers", implying all, but there are 7 numbers for 6 cells, so perhaps one is extra, or I miscount.

Cells to fill: P,Q,R,S,T,U — 6 cells.

Numbers to use: 15,18,22,28,43,46,82 — 7 numbers, so perhaps not all are used, or perhaps 79,21,16 are from the list, but 79 not in list, 21 not, 16 not, so likely the 7 numbers are for the 6 cells, which is odd.

Perhaps "use these numbers" means select from them, not use all.

In that case, for T+U=24, possible pairs from list: 15+9 not, 18+6 not, 22+2 not, 28-4 not, etc. No two add to 24, as min sum is 15+18=33>24.

So impossible.

Perhaps the 103 is for the row, but then U=66 not available.

I think there might be a typo in the problem.

For the sake of providing an answer, I'll solve the parts that are clear and for the squares, I'll make reasonable assumptions or omit.

But let's try the first square with the pair that sums to 46, assuming row sum is 88.

Suppose row1 sum is 88, then A+B=46, and from list, 10+36=46 or 17+29=46.

Say A=10, B=36.

Then col1: 42+C+F=101 → C+F=59, possible 17+42 but 42 used, or 29+30 not, 50+9 not, 59+0 not. 17+42 not, 29+30 not, 50+9 not, 59+0 not. From list, 17+42 not, 29+30 not, 50+9 not, 59+0 not. 16+43 not, etc. 59 is in list, but 59+0 not. 50+9 not. 29+30 not. 17+42 not. 10+49 not. Perhaps 59 and 0, not.

C+F=59, possible 50+9 not, 59+0 not, 29+30 not, 17+42 not, 16+43 not, 21+38 not, 36+23 not, 10+49 not. No pair from remaining numbers.

If A=17, B=29, then A+B=46.

Then C+F=59, same issue.

So not working.

Perhaps the column sum 101 is for something else.

I recall that in some puzzles, the number below is the sum of the column, but for the first column, 42 + C + F = 101, so C+F=59, and if we have 50 and 9, but 9 not in list.

Unless 59 is used, but 59+0 not.

Perhaps 59 is for C or F, but then the other is 0, not in list.

I think I need to accept that for the squares, there might be errors, and focus on the other