Integers Worksheet -- Adding Integers from (-9) to (+9) (All ... - Free Printable

Problem Description:

The task involves solving a series of integer addition problems. The goal is to add two integers (positive or negative) and determine the result using basic arithmetic rules for adding integers.

Solution Approach:

To solve these problems, we need to follow these rules for adding integers:
1. Adding two positive integers: Add their absolute values, and the result is positive.
2. Adding two negative integers: Add their absolute values, and the result is negative.
3. Adding a positive and a negative integer:
- Subtract the smaller absolute value from the larger absolute value.
- The sign of the result will be the same as the integer with the larger absolute value.

Step-by-Step Solutions:

#### First Row:
1. $(-2) + (+8)$:
- Absolute values: $|-2| = 2$, $|+8| = 8$.
- Since $8 > 2$, subtract $2$ from $8$: $8 - 2 = 6$.
- The larger absolute value is $8$, which is positive, so the result is positive.
- Answer: $+6$.

2. $(+9) + (+7)$:
- Both are positive, so add their absolute values: $9 + 7 = 16$.
- Answer: $+16$.

3. $(+7) + (-1)$:
- Absolute values: $|+7| = 7$, $|-1| = 1$.
- Since $7 > 1$, subtract $1$ from $7$: $7 - 1 = 6$.
- The larger absolute value is $7$, which is positive, so the result is positive.
- Answer: $+6$.

#### Second Row:
4. $(+3) + (+1)$:
- Both are positive, so add their absolute values: $3 + 1 = 4$.
- Answer: $+4$.

5. $(+7) + (+5)$:
- Both are positive, so add their absolute values: $7 + 5 = 12$.
- Answer: $+12$.

6. $(-5) + (+9)$:
- Absolute values: $|-5| = 5$, $|+9| = 9$.
- Since $9 > 5$, subtract $5$ from $9$: $9 - 5 = 4$.
- The larger absolute value is $9$, which is positive, so the result is positive.
- Answer: $+4$.

#### Third Row:
7. $(+2) + (-5)$:
- Absolute values: $|+2| = 2$, $|-5| = 5$.
- Since $5 > 2$, subtract $2$ from $5$: $5 - 2 = 3$.
- The larger absolute value is $5$, which is negative, so the result is negative.
- Answer: $-3$.

8. $(-1) + (+3)$:
- Absolute values: $|-1| = 1$, $|+3| = 3$.
- Since $3 > 1$, subtract $1$ from $3$: $3 - 1 = 2$.
- The larger absolute value is $3$, which is positive, so the result is positive.
- Answer: $+2$.

9. $(+8) + (+4)$:
- Both are positive, so add their absolute values: $8 + 4 = 12$.
- Answer: $+12$.

#### Fourth Row:
10. $(-7) + (-2)$:
- Both are negative, so add their absolute values: $7 + 2 = 9$.
- The result is negative.
- Answer: $-9$.

11. $(-6) + (-7)$:
- Both are negative, so add their absolute values: $6 + 7 = 13$.
- The result is negative.
- Answer: $-13$.

12. $(+7) + (+8)$:
- Both are positive, so add their absolute values: $7 + 8 = 15$.
- Answer: $+15$.

#### Fifth Row:
13. $(-4) + (+3)$:
- Absolute values: $|-4| = 4$, $|+3| = 3$.
- Since $4 > 3$, subtract $3$ from $4$: $4 - 3 = 1$.
- The larger absolute value is $4$, which is negative, so the result is negative.
- Answer: $-1$.

14. $(-2) + (-6)$:
- Both are negative, so add their absolute values: $2 + 6 = 8$.
- The result is negative.
- Answer: $-8$.

15. $(+9) + (-4)$:
- Absolute values: $|+9| = 9$, $|-4| = 4$.
- Since $9 > 4$, subtract $4$ from $9$: $9 - 4 = 5$.
- The larger absolute value is $9$, which is positive, so the result is positive.
- Answer: $+5$.

#### Sixth Row:
16. $(+7) + (+3)$:
- Both are positive, so add their absolute values: $7 + 3 = 10$.
- Answer: $+10$.

17. $(-5) + (-9)$:
- Both are negative, so add their absolute values: $5 + 9 = 14$.
- The result is negative.
- Answer: $-14$.

18. $(-5) + (-6)$:
- Both are negative, so add their absolute values: $5 + 6 = 11$.
- The result is negative.
- Answer: $-11$.

#### Seventh Row:
19. $(-9) + (-4)$:
- Both are negative, so add their absolute values: $9 + 4 = 13$.
- The result is negative.
- Answer: $-13$.

20. $(-5) + (+4)$:
- Absolute values: $|-5| = 5$, $|+4| = 4$.
- Since $5 > 4$, subtract $4$ from $5$: $5 - 4 = 1$.
- The larger absolute value is $5$, which is negative, so the result is negative.
- Answer: $-1$.

21. $(-3) + (-9)$:
- Both are negative, so add their absolute values: $3 + 9 = 12$.
- The result is negative.
- Answer: $-12$.

#### Eighth Row:
22. $(-7) + (+1)$:
- Absolute values: $|-7| = 7$, $|+1| = 1$.
- Since $7 > 1$, subtract $1$ from $7$: $7 - 1 = 6$.
- The larger absolute value is $7$, which is negative, so the result is negative.
- Answer: $-6$.

23. $(-1) + (-8)$:
- Both are negative, so add their absolute values: $1 + 8 = 9$.
- The result is negative.
- Answer: $-9$.

24. $(-7) + (-4)$:
- Both are negative, so add their absolute values: $7 + 4 = 11$.
- The result is negative.
- Answer: $-11$.

#### Ninth Row:
25. $(-1) + (+4)$:
- Absolute values: $|-1| = 1$, $|+4| = 4$.
- Since $4 > 1$, subtract $1$ from $4$: $4 - 1 = 3$.
- The larger absolute value is $4$, which is positive, so the result is positive.
- Answer: $+3$.

26. $(+7) + (-4)$:
- Absolute values: $|+7| = 7$, $|-4| = 4$.
- Since $7 > 4$, subtract $4$ from $7$: $7 - 4 = 3$.
- The larger absolute value is $7$, which is positive, so the result is positive.
- Answer: $+3$.

27. $(-6) + (+9)$:
- Absolute values: $|-6| = 6$, $|+9| = 9$.
- Since $9 > 6$, subtract $6$ from $9$: $9 - 6 = 3$.
- The larger absolute value is $9$, which is positive, so the result is positive.
- Answer: $+3$.

#### Tenth Row:
28. $(-4) + (-1)$:
- Both are negative, so add their absolute values: $4 + 1 = 5$.
- The result is negative.
- Answer: $-5$.

29. $(+9) + (+3)$:
- Both are positive, so add their absolute values: $9 + 3 = 12$.
- Answer: $+12$.

30. $(+2) + (-5)$:
- Absolute values: $|+2| = 2$, $|-5| = 5$.
- Since $5 > 2$, subtract $2$ from $5$: $5 - 2 = 3$.
- The larger absolute value is $5$, which is negative, so the result is negative.
- Answer: $-3$.

Final Answer:

The solutions match the provided answers in the image. Therefore, the final answer is:

\boxed{\text{All answers are correct as shown in the image.}}