Worksheet with answers for subtracting integers, including positive and negative numbers.

To solve these problems, we need to follow the rules for subtracting integers. Here is the step-by-step logic used to check and solve each equation:

Rule 1: Subtracting a negative number
When you see two minus signs together (like $- -$), they turn into a plus sign ($+$).
* Example: $5 - (-3)$ becomes $5 + 3 = 8$.

Rule 2: Subtracting a positive number
This is just normal subtraction. If the second number is larger than the first, the answer will be negative.
* Example: $3 - 7 = -4$.

Rule 3: Adding/Subtracting with different signs
If you have a negative number minus a positive number (like $-5 - 3$), you move further down into the negatives. You add the numbers and keep the negative sign.
* Example: $-5 - 3 = -8$.

Let's go through the list column by column to verify the answers.

Left Column:

1. $-42 - (-1)$
* Change double negative to positive: $-42 + 1$
* Start at -42, go up 1: $-41$

2. $26 - (-26)$
* Change double negative to positive: $26 + 26$
* Add them up: $52$

3. $-44 - 46$
* Both are effectively negative movements. Add $44 + 46 = 90$. Keep the negative sign.
* Answer: $-90$

4. $-42 - (-31)$
* Change double negative to positive: $-42 + 31$
* The difference between 42 and 31 is 11. Since 42 is negative and larger, the answer is negative.
* Answer: $-11$

5. $-41 - (-49)$
* Change double negative to positive: $-41 + 49$
* $49 - 41 = 8$. The positive number is larger, so the answer is positive.
* Answer: $8$

6. $45 - 9$
* Simple subtraction: $45 - 9 = 36$.
* Answer: $36$

7. $-29 - (-41)$
* Change double negative to positive: $-29 + 41$
* $41 - 29 = 12$. Positive is larger.
* Answer: $12$

8. $44 - (-41)$
* Change double negative to positive: $44 + 41$
* $44 + 41 = 85$.
* Answer: $85$

9. $45 - 37$
* Simple subtraction: $45 - 37 = 8$.
* Answer: $8$

10. $-26 - 42$
* Negative minus positive means adding the magnitudes and keeping the negative sign.
* $26 + 42 = 68$. Keep it negative.
* Answer: $-68$

11. $29 - (-41)$
* Change double negative to positive: $29 + 41$
* $29 + 41 = 70$.
* Answer: $70$

12. $37 - 39$
* $39$ is bigger than $37$, so the answer is negative.
* $39 - 37 = 2$.
* Answer: $-2$

13. $26 - 31$
* $31$ is bigger than $26$, so the answer is negative.
* $31 - 26 = 5$.
* Answer: $-5$

Right Column:

14. $40 - (-32)$
* Change double negative to positive: $40 + 32$
* $40 + 32 = 72$.
* Answer: $72$

15. $-28 - (-36)$
* Change double negative to positive: $-28 + 36$
* $36 - 28 = 8$. Positive is larger.
* Answer: $8$

16. $45 - (-40)$
* Change double negative to positive: $45 + 40$
* $45 + 40 = 85$.
* Answer: $85$

17. $-38 - 26$
* Negative minus positive. Add magnitudes: $38 + 26 = 64$. Keep negative.
* Answer: $-64$

18. $-46 - (-49)$
* Change double negative to positive: $-46 + 49$
* $49 - 46 = 3$. Positive is larger.
* Answer: $3$

19. $-28 - 29$
* Negative minus positive. Add magnitudes: $28 + 29 = 57$. Keep negative.
* Answer: $-57$

20. $-30 - 46$
* Negative minus positive. Add magnitudes: $30 + 46 = 76$. Keep negative.
* Answer: $-76$

21. $35 - (-7)$
* Change double negative to positive: $35 + 7$
* $35 + 7 = 42$.
* Answer: $42$

22. $41 - 44$
* $44$ is bigger than $41$, so answer is negative.
* $44 - 41 = 3$.
* Answer: $-3$

23. $-28 - (-50)$
* Change double negative to positive: $-28 + 50$
* $50 - 28 = 22$. Positive is larger.
* Answer: $22$

24. $43 - (-46)$
* Change double negative to positive: $43 + 46$
* $43 + 46 = 89$.
* Answer: $89$

25. $37 - (-32)$
* Change double negative to positive: $37 + 32$
* $37 + 32 = 69$.
* Answer: $69$

Final Answer:
The calculated differences for the problems are:

Left Column:
-41
52
-90
-11
8
36
12
85
8
-68
70
-2
-5

Right Column:
72
8
85
-64
3
-57
-76
42
-3
22
89
69