9 Adding and Subtracting Integers Worksheets to Teach with ... - Free Printable

Problem Overview:

The task involves solving a series of integer addition and subtraction problems. The goal is to compute the results of each expression accurately, keeping in mind the rules for adding and subtracting integers.

Key Rules for Integer Operations:

1. Addition:
- Adding two positive integers: Add their absolute values, and the result is positive.
- Adding two negative integers: Add their absolute values, and the result is negative.
- Adding a positive and a negative integer: Subtract the smaller absolute value from the larger one, and the sign of the result matches the number with the larger absolute value.

2. Subtraction:
- Subtracting an integer is equivalent to adding its opposite. For example, \( a - b = a + (-b) \).

Solution to Each Problem:

#### Section 1: Addition
1. \( (-90) + (-10) \)
- Both numbers are negative. Add their absolute values: \( 90 + 10 = 100 \).
- Result: \( -100 \).

2. \( (459) + (254) \)
- Both numbers are positive. Add their values: \( 459 + 254 = 713 \).
- Result: \( 713 \).

3. \( (-7) + (242) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 242 - 7 = 235 \).
- The larger absolute value is \( 242 \), which is positive.
- Result: \( 235 \).

4. \( (71) + (180) \)
- Both numbers are positive. Add their values: \( 71 + 180 = 251 \).
- Result: \( 251 \).

5. \( (-333) + (-211) \)
- Both numbers are negative. Add their absolute values: \( 333 + 211 = 544 \).
- Result: \( -544 \).

6. \( (-312) - (471) \)
- Subtracting \( 471 \) is the same as adding \( -471 \): \( -312 + (-471) \).
- Both numbers are negative. Add their absolute values: \( 312 + 471 = 783 \).
- Result: \( -783 \).

7. \( (-161) - (-374) \)
- Subtracting \( -374 \) is the same as adding \( 374 \): \( -161 + 374 \).
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 374 - 161 = 213 \).
- The larger absolute value is \( 374 \), which is positive.
- Result: \( 213 \).

8. \( (-232) - (-107) \)
- Subtracting \( -107 \) is the same as adding \( 107 \): \( -232 + 107 \).
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 232 - 107 = 125 \).
- The larger absolute value is \( 232 \), which is negative.
- Result: \( -125 \).

9. \( (381) + (298) \)
- Both numbers are positive. Add their values: \( 381 + 298 = 679 \).
- Result: \( 679 \).

10. \( (-173) + (450) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 450 - 173 = 277 \).
- The larger absolute value is \( 450 \), which is positive.
- Result: \( 277 \).

11. \( (-181) + (292) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 292 - 181 = 111 \).
- The larger absolute value is \( 292 \), which is positive.
- Result: \( 111 \).

12. \( (239) + (-105) \)
- One number is positive, and the other is negative. Subtract the smaller absolute value from the larger one: \( 239 - 105 = 134 \).
- The larger absolute value is \( 239 \), which is positive.
- Result: \( 134 \).

#### Section 2: Subtraction
13. \( (-160) - (-463) \)
- Subtracting \( -463 \) is the same as adding \( 463 \): \( -160 + 463 \).
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 463 - 160 = 303 \).
- The larger absolute value is \( 463 \), which is positive.
- Result: \( 303 \).

14. \( (140) - (140) \)
- Subtracting \( 140 \) from \( 140 \): \( 140 - 140 = 0 \).
- Result: \( 0 \).

15. \( (119) + (55) \)
- Both numbers are positive. Add their values: \( 119 + 55 = 174 \).
- Result: \( 174 \).

16. \( (-276) - (-14) \)
- Subtracting \( -14 \) is the same as adding \( 14 \): \( -276 + 14 \).
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 276 - 14 = 262 \).
- The larger absolute value is \( 276 \), which is negative.
- Result: \( -262 \).

17. \( (475) - (-155) \)
- Subtracting \( -155 \) is the same as adding \( 155 \): \( 475 + 155 \).
- Both numbers are positive. Add their values: \( 475 + 155 = 630 \).
- Result: \( 630 \).

18. \( (67) - (77) \)
- Subtracting \( 77 \) from \( 67 \): \( 67 - 77 = -10 \).
- Result: \( -10 \).

19. \( (-243) + (-385) \)
- Both numbers are negative. Add their absolute values: \( 243 + 385 = 628 \).
- Result: \( -628 \).

20. \( (381) - (70) \)
- Subtracting \( 70 \) from \( 381 \): \( 381 - 70 = 311 \).
- Result: \( 311 \).

21. \( (-307) - (340) \)
- Subtracting \( 340 \) is the same as adding \( -340 \): \( -307 + (-340) \).
- Both numbers are negative. Add their absolute values: \( 307 + 340 = 647 \).
- Result: \( -647 \).

22. \( (-453) + (421) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 453 - 421 = 32 \).
- The larger absolute value is \( 453 \), which is negative.
- Result: \( -32 \).

23. \( (-37) + (-489) \)
- Both numbers are negative. Add their absolute values: \( 37 + 489 = 526 \).
- Result: \( -526 \).

24. \( (-121) + (+443) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 443 - 121 = 322 \).
- The larger absolute value is \( 443 \), which is positive.
- Result: \( 322 \).

25. \( (-300) + (452) \)
- One number is negative, and the other is positive. Subtract the smaller absolute value from the larger one: \( 452 - 300 = 152 \).
- The larger absolute value is \( 452 \), which is positive.
- Result: \( 152 \).

26. \( (198) - (-190) \)
- Subtracting \( -190 \) is the same as adding \( 190 \): \( 198 + 190 \).
- Both numbers are positive. Add their values: \( 198 + 190 = 388 \).
- Result: \( 388 \).

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -100 \\
2. & 713 \\
3. & 235 \\
4. & 251 \\
5. & -544 \\
6. & -783 \\
7. & 213 \\
8. & -125 \\
9. & 679 \\
10. & 277 \\
11. & 111 \\
12. & 134 \\
13. & 303 \\
14. & 0 \\
15. & 174 \\
16. & -262 \\
17. & 630 \\
18. & -10 \\
19. & -628 \\
20. & 311 \\
21. & -647 \\
22. & -32 \\
23. & -526 \\
24. & 322 \\
25. & 152 \\
26. & 388 \\
\end{array}
}
\]