Integer operations practice worksheet for math students.
Worksheet for practicing adding, subtracting, multiplying, and dividing integers with problems and space for answers.
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Step-by-step solution for: Integers Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Integers Worksheets
The image you uploaded is a worksheet titled "Adding, Subtracting, Multiplying, and Dividing Integers (A)." It contains a series of arithmetic problems involving integers. Below, I will solve each problem step by step and explain the solution.
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#### 1. Addition
1. 0 + (-1) = -1
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 0 + (-1) = -1 \).
2. -6 + (-6) = -12
- Adding two negative numbers results in a larger negative number.
- \( -6 + (-6) = -12 \).
3. -72 + (-9) = -81
- Adding two negative numbers results in a larger negative number.
- \( -72 + (-9) = -81 \).
4. -5 + (-6) = -11
- Adding two negative numbers results in a larger negative number.
- \( -5 + (-6) = -11 \).
5. -4 + (-8) = -12
- Adding two negative numbers results in a larger negative number.
- \( -4 + (-8) = -12 \).
6. -7 + (-4) = -11
- Adding two negative numbers results in a larger negative number.
- \( -7 + (-4) = -11 \).
7. -40 + (-4) = -44
- Adding two negative numbers results in a larger negative number.
- \( -40 + (-4) = -44 \).
8. 14 + (-2) = 12
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 14 + (-2) = 14 - 2 = 12 \).
9. 1 + (-1) = 0
- Adding a number and its opposite results in zero.
- \( 1 + (-1) = 0 \).
10. 7 + (-2) = 5
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 7 + (-2) = 7 - 2 = 5 \).
11. 6 + (-2) = 4
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 6 + (-2) = 6 - 2 = 4 \).
12. 1 + (-9) = -8
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 1 + (-9) = 1 - 9 = -8 \).
13. 9 + (-9) = 0
- Adding a number and its opposite results in zero.
- \( 9 + (-9) = 0 \).
14. -3 + (-9) = -12
- Adding two negative numbers results in a larger negative number.
- \( -3 + (-9) = -12 \).
15. -1 + (-9) = -10
- Adding two negative numbers results in a larger negative number.
- \( -1 + (-9) = -10 \).
16. -42 + (-6) = -48
- Adding two negative numbers results in a larger negative number.
- \( -42 + (-6) = -48 \).
#### 2. Subtraction
17. -6 - 2 = -8
- Subtracting a positive number from a negative number makes the result more negative.
- \( -6 - 2 = -8 \).
18. -7 - (-4) = -3
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -7 - (-4) = -7 + 4 = -3 \).
19. -9 - (-3) = -6
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -9 - (-3) = -9 + 3 = -6 \).
20. -3 - (-2) = -1
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-2) = -3 + 2 = -1 \).
21. 1 - 3 = -2
- Subtracting a larger positive number from a smaller positive number results in a negative number.
- \( 1 - 3 = -2 \).
22. -9 - 8 = -17
- Subtracting a positive number from a negative number makes the result more negative.
- \( -9 - 8 = -17 \).
23. 56 + (-4) = 52
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 56 + (-4) = 56 - 4 = 52 \).
24. 1 + (-6) = -5
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 1 + (-6) = 1 - 6 = -5 \).
25. 3 - (-3) = 6
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 3 - (-3) = 3 + 3 = 6 \).
26. 6 - 6 = 0
- Subtracting a number from itself results in zero.
- \( 6 - 6 = 0 \).
27. 40 - (-7) = 47
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 40 - (-7) = 40 + 7 = 47 \).
28. 2 - 2 = 0
- Subtracting a number from itself results in zero.
- \( 2 - 2 = 0 \).
29. 8 - 3 = 5
- Subtracting a smaller positive number from a larger positive number results in a positive number.
- \( 8 - 3 = 5 \).
30. -3 - (-3) = 0
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-3) = -3 + 3 = 0 \).
31. -4 - (-2) = -2
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -4 - (-2) = -4 + 2 = -2 \).
32. -2 - 7 = -9
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 7 = -9 \).
33. -2 - 3 = -5
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 3 = -5 \).
34. -20 - 0 = -20
- Subtracting zero from any number leaves the number unchanged.
- \( -20 - 0 = -20 \).
35. -2 - 7 = -9
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 7 = -9 \).
36. -3 - (-8) = 5
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-8) = -3 + 8 = 5 \).
37. -8 - (-8) = 0
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -8 - (-8) = -8 + 8 = 0 \).
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The solutions to all the problems are provided above. If you need further clarification on any specific problem, feel free to ask!
Boxed Final Answer:
\[
\boxed{\text{See detailed solutions above.}}
\]
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Worksheet Problems and Solutions
#### 1. Addition
1. 0 + (-1) = -1
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 0 + (-1) = -1 \).
2. -6 + (-6) = -12
- Adding two negative numbers results in a larger negative number.
- \( -6 + (-6) = -12 \).
3. -72 + (-9) = -81
- Adding two negative numbers results in a larger negative number.
- \( -72 + (-9) = -81 \).
4. -5 + (-6) = -11
- Adding two negative numbers results in a larger negative number.
- \( -5 + (-6) = -11 \).
5. -4 + (-8) = -12
- Adding two negative numbers results in a larger negative number.
- \( -4 + (-8) = -12 \).
6. -7 + (-4) = -11
- Adding two negative numbers results in a larger negative number.
- \( -7 + (-4) = -11 \).
7. -40 + (-4) = -44
- Adding two negative numbers results in a larger negative number.
- \( -40 + (-4) = -44 \).
8. 14 + (-2) = 12
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 14 + (-2) = 14 - 2 = 12 \).
9. 1 + (-1) = 0
- Adding a number and its opposite results in zero.
- \( 1 + (-1) = 0 \).
10. 7 + (-2) = 5
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 7 + (-2) = 7 - 2 = 5 \).
11. 6 + (-2) = 4
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 6 + (-2) = 6 - 2 = 4 \).
12. 1 + (-9) = -8
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 1 + (-9) = 1 - 9 = -8 \).
13. 9 + (-9) = 0
- Adding a number and its opposite results in zero.
- \( 9 + (-9) = 0 \).
14. -3 + (-9) = -12
- Adding two negative numbers results in a larger negative number.
- \( -3 + (-9) = -12 \).
15. -1 + (-9) = -10
- Adding two negative numbers results in a larger negative number.
- \( -1 + (-9) = -10 \).
16. -42 + (-6) = -48
- Adding two negative numbers results in a larger negative number.
- \( -42 + (-6) = -48 \).
#### 2. Subtraction
17. -6 - 2 = -8
- Subtracting a positive number from a negative number makes the result more negative.
- \( -6 - 2 = -8 \).
18. -7 - (-4) = -3
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -7 - (-4) = -7 + 4 = -3 \).
19. -9 - (-3) = -6
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -9 - (-3) = -9 + 3 = -6 \).
20. -3 - (-2) = -1
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-2) = -3 + 2 = -1 \).
21. 1 - 3 = -2
- Subtracting a larger positive number from a smaller positive number results in a negative number.
- \( 1 - 3 = -2 \).
22. -9 - 8 = -17
- Subtracting a positive number from a negative number makes the result more negative.
- \( -9 - 8 = -17 \).
23. 56 + (-4) = 52
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 56 + (-4) = 56 - 4 = 52 \).
24. 1 + (-6) = -5
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 1 + (-6) = 1 - 6 = -5 \).
25. 3 - (-3) = 6
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 3 - (-3) = 3 + 3 = 6 \).
26. 6 - 6 = 0
- Subtracting a number from itself results in zero.
- \( 6 - 6 = 0 \).
27. 40 - (-7) = 47
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 40 - (-7) = 40 + 7 = 47 \).
28. 2 - 2 = 0
- Subtracting a number from itself results in zero.
- \( 2 - 2 = 0 \).
29. 8 - 3 = 5
- Subtracting a smaller positive number from a larger positive number results in a positive number.
- \( 8 - 3 = 5 \).
30. -3 - (-3) = 0
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-3) = -3 + 3 = 0 \).
31. -4 - (-2) = -2
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -4 - (-2) = -4 + 2 = -2 \).
32. -2 - 7 = -9
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 7 = -9 \).
33. -2 - 3 = -5
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 3 = -5 \).
34. -20 - 0 = -20
- Subtracting zero from any number leaves the number unchanged.
- \( -20 - 0 = -20 \).
35. -2 - 7 = -9
- Subtracting a positive number from a negative number makes the result more negative.
- \( -2 - 7 = -9 \).
36. -3 - (-8) = 5
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -3 - (-8) = -3 + 8 = 5 \).
37. -8 - (-8) = 0
- Subtracting a negative number is the same as adding its positive counterpart.
- \( -8 - (-8) = -8 + 8 = 0 \).
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Final Answer
The solutions to all the problems are provided above. If you need further clarification on any specific problem, feel free to ask!
Boxed Final Answer:
\[
\boxed{\text{See detailed solutions above.}}
\]
Parent Tip: Review the logic above to help your child master the concept of 6th grade integers worksheet.
