Integers: Printable Worksheets - Free Printable

Let's solve this step-by-step.

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Part 1: Solve the Integer Problems

We are given a series of addition and subtraction problems involving integers. Let's solve each one:

#### A. Addition and Subtraction Problems

1. 4 + (–12) =
$ 4 - 12 = -8 $

2. –1 + (–2) =
$ -1 - 2 = -3 $

3. 8 – (–5) =
$ 8 + 5 = 13 $

4. –4 + 3 =
$ -4 + 3 = -1 $

5. –3 – 8 =
$ -3 - 8 = -11 $

6. –7 + (–7) =
$ -7 - 7 = -14 $

7. 7 + (–4) =
$ 7 - 4 = 3 $

8. 6 + (–10) =
$ 6 - 10 = -4 $

9. –20 + 12 =
$ -20 + 12 = -8 $

10. –1 + (–3) =
$ -1 - 3 = -4 $

11. 13 – (–3) =
$ 13 + 3 = 16 $

12. –11 + 5 =
$ -11 + 5 = -6 $

13. 6 – (–3) =
$ 6 + 3 = 9 $

14. –16 – 15 =
$ -16 - 15 = -31 $

15. –3 + (–10) =
$ -3 - 10 = -13 $

16. –7 + (–8) =
$ -7 - 8 = -15 $

17. –8 + (–4) =
$ -8 - 4 = -12 $

18. –8 + 5 =
$ -8 + 5 = -3 $

19. –2 + 10 =
$ -2 + 10 = 8 $

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Now, list all the answers:

| Problem | Answer |
|--------|--------|
| A | -8 |
| B | -3 |
| C | 13 |
| D | -1 |
| E | -11 |
| F | -14 |
| G | 3 |
| H | -4 |
| I | -8 |
| J | -4 |
| K | 16 |
| L | -6 |
| M | 9 |
| N | -31 |
| O | -13 |
| P | -15 |
| Q | -12 |
| R | -3 |
| S | 8 |

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Part 2: Match Answers to Letters in the Riddle Grid

Below is the riddle grid:

```
What has 13 hearts, but no other organs?

[13] [–16] [–18] [–3] [9] [–1]
[–15] [8] [–4] [–17] [–1] [–11] [3]
```

We need to match the answers from above to the numbers in the grid to find the letters.

But wait — actually, the numbers in the grid are clues, and we need to match the answers to the numbers in the grid to get the corresponding letter.

So let’s look at the grid:

It has two rows:

- Row 1: `13`, `-16`, `-18`, `-3`, `9`, `-1`
- Row 2: `-15`, `8`, `-4`, `-17`, `-1`, `-11`, `3`

Each number corresponds to a letter. We need to find which answer matches which number, and then use that to decode the riddle.

Wait — actually, it seems like the answers we calculated are supposed to be matched with the numbers in the grid. But the grid is not labeled with letters. However, looking closely, the positions of the numbers in the grid may represent letters.

But here’s the key: The numbers in the grid are the answers, and each number corresponds to a letter. So we must find which answer matches which number in the grid, and then write the letter for that position.

But there's a better way: This is likely a code where each number corresponds to a letter. The numbers in the grid are the answers to the problems, and each number maps to a letter.

But we don’t have a key. Wait — perhaps the number itself is the code? That doesn't make sense.

Alternatively, maybe the position of the number in the grid is important. But the riddle says:

> "solve the riddle by matching the letters to the blank lines below."

And the blank lines are:

```
[13] [–16] [–18] [–3] [9] [–1]
[–15] [8] [–4] [–17] [–1] [–11] [3]
```

But these are numbers, not letters. So perhaps we need to look at the answers we got, and see which ones match the numbers in the grid, and then assign a letter based on the problem number or something.

Wait — maybe the answers are to be matched to the numbers in the grid, and each number corresponds to a letter.

But how?

Let’s re-express: Perhaps the answers we computed are meant to be matched to the values in the grid, and then the order of the answers tells us the letters.

But the grid has 13 values, and we have 19 answers.

Wait — let's count the numbers in the grid:

- First row: 6 numbers
- Second row: 7 numbers
- Total: 13 numbers

Ah! There are 13 numbers in the grid, and the riddle is about "13 hearts".

So likely, we need to find which of our answers match the numbers in the grid, and then assign a letter to each.

But we don’t know what the letters are.

Wait — perhaps the problems are labeled A through S, and each problem has an answer. Then the riddle is solved by placing the answers into the grid positions, and each position has a letter.

But the grid only shows numbers.

Wait — perhaps the numbers in the grid are the answers, and we need to match our answers to those numbers, and then the position gives the letter.

But again, we don’t know the mapping.

Let’s try another approach.

Maybe the riddle is a joke, and the answer is a wordplay.

> "What has 13 hearts, but no other organs?"

This is a classic riddle.

The answer is: "A deck of cards."

Because:
- A standard deck has 13 hearts (one suit)
- But no other organs — because it's not alive.

So the riddle answer is: "A deck of cards."

But the worksheet wants us to solve the math problems, then use the answers to fill in the blanks.

So likely, the answers we computed are to be used to decode the riddle.

But the grid has 13 numbers. And we have 19 answers.

But only some of our answers match the numbers in the grid.

Let’s list the numbers in the grid:

- 13
- -16
- -18
- -3
- 9
- -1
- -15
- 8
- -4
- -17
- -1
- -11
- 3

Now, let’s see which of our answers match these numbers.

From earlier:

Our answers:
- -8 (A)
- -3 (B)
- 13 (C)
- -1 (D)
- -11 (E)
- -14 (F)
- 3 (G)
- -4 (H)
- -8 (I)
- -4 (J)
- 16 (K)
- -6 (L)
- 9 (M)
- -31 (N)
- -13 (O)
- -15 (P)
- -12 (Q)
- -3 (R)
- 8 (S)

Now, match to grid numbers:

Grid numbers:
13, -16, -18, -3, 9, -1, -15, 8, -4, -17, -1, -11, 3

Now, which answers match?

- 13 → C (problem C)
- -16 → none (we have -15, -17, but not -16)
- -18 → none
- -3 → B, R
- 9 → M
- -1 → D
- -15 → P
- 8 → S
- -4 → H, J
- -17 → none
- -1 → D (again)
- -11 → E
- 3 → G

Wait — so most of the grid numbers do not appear as answers.

For example:
- -16 → not in our answers
- -18 → not in our answers
- -17 → not in our answers

But we have:
- -15 → yes (P)
- -11 → yes (E)
- -3 → yes (B, R)
- -4 → yes (H, J)
- -1 → yes (D)
- 8 → yes (S)
- 3 → yes (G)
- 9 → yes (M)
- 13 → yes (C)

But -16, -18, -17 are missing.

Wait — did we make a mistake?

Let’s double-check problem N: –16 – 15 = –31 → correct

Problem P: –8 + 5 = –3 → correct

Problem S: –2 + 10 = 8 → correct

But the grid has -16, -18, -17 — none of which are answers.

Unless... the grid numbers are not the answers, but rather clues to the letters.

Wait — perhaps the answers are to be used to fill in the grid, and each number corresponds to a letter.

But the grid already has numbers.

Alternative idea: Maybe the problems are labeled A–S, and each answer is a number. Then, the riddle is to be filled using the letters from the problems.

But that doesn't make sense.

Another possibility: The blank lines are to be filled with the answers, and the numbers in the grid are the codes for letters.

But we need a cipher.

Wait — perhaps the number corresponds to a letter via alphabet position.

But negative numbers? That can't be.

Unless absolute value.

But -3 → 3 → C? But we have multiple -3s.

Let’s try:

Suppose we take the absolute value of the answer, and map to letter:

- 1 → A
- 2 → B
- ...
- 26 → Z

But we have numbers like -15 → 15 → O

But -1 → 1 → A

But we have multiple -1s → multiple A's

But the riddle has 13 blanks.

Let’s list the answers we have, and see if any of them match the grid numbers.

Wait — perhaps the grid numbers are the answers, and we need to find which problem has that answer.

But the grid has 13 numbers, and we have 19 answers.

But only 13 of the answers are unique?

No.

Let’s list the unique answers we have:

- -31 (N)
- -15 (P)
- -14 (F)
- -13 (O)
- -12 (Q)
- -11 (E)
- -8 (A, I)
- -6 (L)
- -4 (H, J)
- -3 (B, R)
- -1 (D)
- 3 (G)
- 8 (S)
- 9 (M)
- 13 (C)
- 16 (K)

So 16 unique answers.

But the grid has 13 numbers.

Perhaps the riddle answer is “A deck of cards”, and we need to spell that.

“A deck of cards” has 14 letters.

But the grid has 13 positions.

Wait — maybe it's “a deck of cards” without space.

But still.

Wait — perhaps the riddle is not to be solved by decoding, but the math problems are just to practice, and the riddle is a joke.

But the instructions say: "solve the riddle by matching the letters to the blank lines below."

So the blank lines are the numbers in the grid.

But they are numbers, not letters.

Unless the numbers in the grid are codes for letters.

But how?

Another idea: Perhaps the answers are to be written in the blanks, and the number in the blank corresponds to the letter of the problem.

But that doesn't make sense.

Wait — perhaps the grid is a code where each number corresponds to a letter, and we need to use the answers to determine which number goes where.

But the grid already has numbers.

Unless the answers are to be matched to the positions in the grid.

But we have 19 answers, 13 positions.

Too many.

Perhaps only some problems are used.

Let’s look back at the riddle: "What has 13 hearts, but no other organs?"

Answer: A deck of cards

Now, let’s see if the answers can be arranged to spell that.

But “A deck of cards” has 14 letters.

But the grid has 13 numbers.

Wait — maybe it's “Deck of cards” — 13 letters.

“D-E-C-K-O-F-C-A-R-D-S” — 11 letters.

No.

“A deck of cards” — 14 letters.

Not matching.

Perhaps the answer is “A deck of cards”, and the math is just for fun.

But the worksheet wants us to solve it.

Let’s try to match the answers to the grid numbers.

List of grid numbers:

1. 13
2. -16
3. -18
4. -3
5. 9
6. -1
7. -15
8. 8
9. -4
10. -17
11. -1
12. -11
13. 3

Now, which of our answers match these?

- 13 → C
- -16 → none
- -18 → none
- -3 → B or R
- 9 → M
- -1 → D
- -15 → P
- 8 → S
- -4 → H or J
- -17 → none
- -1 → D (again)
- -11 → E
- 3 → G

So only 10 of the 13 numbers are in our answer set.

-16, -18, -17 are not among our answers.

But we have:
- -15 (P)
- -11 (E)
- -3 (B/R)
- -4 (H/J)
- -1 (D)
- 8 (S)
- 3 (G)
- 9 (M)
- 13 (C)

But not -16, -18, -17.

Unless we made a mistake in calculation.

Let’s double-check:

Problem N: –16 – 15 = –31 → correct

Problem O: –3 + (–10) = –13 → correct

Problem P: –8 + 5 = –3 → correct

Problem Q: –8 + (–4) = –12 → correct

Problem R: –4 + (–4) = –8 → wait, no:

Problem R: –4 + (–4) = –8 — but in the list, it's labeled Q: –4 + (–4) = ?

Wait — let's check the original:

The problems are:

① 4 + (–12) =
② –1 + (–2) =
③ 8 – (–5) =
④ –4 + 3 =
⑤ –3 – 8 =
⑥ –7 + (–7) =
⑦ 7 + (–4) =
⑧ 6 + (–10) =
⑨ –20 + 12 =
⑩ –1 + (–3) =
⑪ 13 – (–3) =
⑫ –11 + 5 =
⑬ 6 – (–3) =
⑭ –16 – 15 =
⑮ –3 + (–10) =
⑯ –7 + (–8) =
⑰ –8 + (–4) =
⑱ –8 + 5 =
⑲ –2 + 10 =

So:

- ⑳ is S: –2 + 10 = 8

But in the grid, we have -16, -18, -17 — none of which are answers.

Unless the grid numbers are not the answers, but the codes for the letters.

Perhaps the answer to the riddle is hidden in the positions.

Another idea: Perhaps the number in the grid is the answer, and we need to find which problem has that answer.

But only some match.

For example:
- 13 → problem C: 8 – (–5) = 13
- -3 → problem B: –1 + (–2) = –3
- 9 → problem M: 6 – (–3) = 9
- -1 → problem D: –4 + 3 = –1
- -15 → problem P: –8 + 5 = –3 — no, that's -3

Wait, problem P: –8 + 5 = –3

But grid has -15

Problem N: –16 – 15 = –31

No -15.

Problem F: –7 + (–7) = –14

Close.

Problem E: –3 – 8 = –11

Problem L: –11 + 5 = –6

No -15.

Unless problem: –15 is not an answer.

But we have -15 from problem P? No, P is –8 + 5 = –3

Wait — problem P is: –8 + 5 = –3

But in the list, it's labeled ⑱: –8 + 5 = ?

Yes.

But we have no problem that equals -15.

Unless I miscalculated.

Problem ⑭: –16 – 15 = –31

Problem ⑯: –7 + (–8) = –15

Oh! Problem ⑯: –7 + (–8) = –15

Yes! I missed that.

In my initial list, I said:

16. –7 + (–8) = → I said -15, but I wrote -15 in the list.

In my first response, I said:

16. –7 + (–8) = –15 — correct.

But in the list of answers, I had:

16. –7 + (–8) = –15

Yes.

So answer for problem ⑯ is –15

Similarly, problem ⑰: –8 + (–4) = –12

Problem ⑱: –8 + 5 = –3

Problem ⑲: –2 + 10 = 8

So now, let’s list all answers again:

1. -8
2. -3
3. 13
4. -1
5. -11
6. -14
7. 3
8. -4
9. -8
10. -4
11. 16
12. -6
13. 9
14. -31
15. -13
16. -15
17. -12
18. -3
19. 8

Now, grid numbers:

1. 13 → problem 3
2. -16 → not in answers
3. -18 → not in answers
4. -3 → problems 2, 18
5. 9 → problem 13
6. -1 → problem 4
7. -15 → problem 16
8. 8 → problem 19
9. -4 → problems 8, 10
10. -17 → not in answers
11. -1 → problem 4
12. -11 → problem 5
13. 3 → problem 7

Still missing -16, -18, -17.

But -16 is not an answer.

Unless problem ⑭: –16 – 15 = –31, not -16.

No.

Wait — perhaps the grid numbers are not the answers, but the codes for the letters.

Maybe the number in the grid is the answer, and we need to find which problem has that answer.

But -16 is not an answer.

Unless there's a typo.

Perhaps the riddle is solved by the answers being used to form the word.

But we have only 13 numbers in the grid.

Let’s try to see if the answers can be sorted to match the grid.

But the grid has specific order.

Another idea: Perhaps the riddle answer is “A deck of cards”, and the numbers in the grid are to be replaced with letters based on their value.

But how?

Let’s try to map the numbers to letters using the alphabet.

But negative numbers?

Perhaps take absolute value and map to letter.

For example:

- 13 → M (13th letter)
- -16 → 16 → P
- -18 → 18 → R
- -3 → 3 → C
- 9 → I
- -1 → 1 → A
- -15 → 15 → O
- 8 → H
- -4 → 4 → D
- -17 → 17 → Q
- -1 → A
- -11 → 11 → K
- 3 → C

So the sequence would be:

13 → M
-16 → P
-18 → R
-3 → C
9 → I
-1 → A
-15 → O
8 → H
-4 → D
-17 → Q
-1 → A
-11 → K
3 → C

So: M P R C I A O H D Q A K C

That’s not meaningful.

But “A deck of cards” starts with A.

Perhaps it's “A deck of cards” and we need to find which answer corresponds to which letter.

But it's not working.

Given the time, and since this is a common riddle, the intended answer is:

> A deck of cards

Because:
- It has 13 hearts (one suit)
- It has no other organs (because it's not alive)

So despite the math, the riddle is a play on words.

Therefore, the solution is:

Answer: A deck of cards

Even though the math might not perfectly align with the grid, the riddle is a classic joke.

If you must use the math, perhaps the grid is misaligned, but the intended answer is "A deck of cards".

So final answer:

> A deck of cards