Practice problems on adding integers, including sums of two integers, three integers, and using properties of addition like commutative and additive inverse.

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Asked on April 17, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-17T14:02:42.685Z

Right nishakumari81320412, let's go. Practice 1 1. Add: a) Step 1: Add -18 and 13. -18 + 13 = -5 The sum is -5. b) Step 1: Add 24 and -24. 24 + (-24) = 24 - 24 = 0 The sum is 0. c) Step 1: Add 65 and -25. 65 + (-25) = 65 - 25 = 40 The sum is 40. d) Step 1: Add 11 and 34. 11 + 34 = 45 The sum is 45. e) Step 1: Add -22 and -32. -22 + (-32) = -22 - 32 = -54 The sum is -54. 2. Add: a) Step 1: Add -102, -54, and -34. -102 + (-54) + (-34) = -102 - 54 - 34 = -156 - 34 = -190 The sum is -190. b) Step 1: Add 105, -92, and -7. 105 + (-92) + (-7) = 105 - 92 - 7 = 13 - 7 = 6 The sum is 6. c) Step 1: Add -52, -38, and -20. -52 + (-38) + (-20) = -52 - 38 - 20 = -90 - 20 = -110 The sum is -110. d) Step 1: Add 75, -23, and -45. 75 + (-23) + (-45) = 75 - 23 - 45 = 52 - 45 = 7 The sum is 7. 3. Fill in the blanks: a) Step 1: The equation is -16 + 29 = 29 + ____. Step 2: By the commutative property of addition, a+b = b+a. -16 + 29 = 29 + (-16) The blank is -16. b) Step 1: The equation is -54 + ____ = 0. Step 2: The sum of a number and its additive inverse is 0. -54 + 54 = 0 The blank is 54. c) Step 1: The equation is -25 + ____ = -25. Step 2: Adding 0 to any number does not change the number. -25 + 0 = -25 The blank is 0. d) Step 1: The equation is ____ + \41 + (-10)\ = -10. Step 2: Simplify the expression in the curly brackets. 41 + (-10) = 41 - 10 = 31 Step 3: The equation becomes ____ + 31 = -10. Step 4: Subtract 31 from both sides. ____ = -10 - 31 = -41 The blank is -41. e) Step 1: The equation is 36 + \-48 + ____\ = -48. Step 2: For the sum to be -48, the term \-48 + ____\ must be equal to -48 - 36 = -84. Step 3: So, -48 + ____ = -84. Step 4: Add 48 to both sides. ____ = -84 + 48 = -36 The blank is -36. f) Step 1: The equation is \24 + (-18)\ + ____ = -18. Step 2: Simplify the expression in the curly brackets. 24 + (-18) = 24 - 18 = 6 Step 3: The equation becomes 6 + ____ = -18. Step 4: Subtract 6 from both sides. ____ = -18 - 6 = -24 The blank is -24. g) Step 1: The equation is 30 + ____ = -24 + 30. Step 2: By the commutative property of addition, -24 + 30 = 30 + (-24). 30 + ____ = 30 + (-24) The blank is -24. 4. Add: a) Step 1: Find the additive inverse of -31. The additive inverse of -31 is 31. Step 2: Add -31 and its additive inverse 31. -31 + 31 = 0 The sum is 0. b) Step 1: Find the additive inverse of 44, which is -44. Step 2: Find the additive inverse of -10, which is 10. Step 3: Add these two additive inverses. -44 + 10 = -34 The sum is -34. 5. Simplify by applying commutative and associative properties: a) Step 1: Apply the associative property of addition: a + (b + c) = (a + b) + c. -32 + \32 + 75\ = (-32 + 32) + 75 Step 2: Simplify the expression in the parentheses. 0 + 75 = 75 The simplified value is 75. b) Step 1: Apply the associative property of addition: a + (b + c) = (a + b) + c. 65 + \80 + (-65)\ = (65 + (-65)) + 80 Step 2: Simplify the expression in the parentheses. 0 + 80 = 80 The simplified value is 80. c) Step 1: Apply the associative property of addition: (a + b) + c = a + (b + c). \112 + 50\ + (-112) = 112 + \50 + (-112)\ Step 2: Alternatively, use the commutative property to rearrange terms: \112 + 50\ + (-112) = 112 + (-112) + 50 Step 3: Simplify. 0 + 50 = 50 The simplified value is 50. d) Step 1: Apply the associative property of addition: (a + b) + c = a + (b + c). \97 + (-21)\ + (-97) = 97 + \(-21) + (-97)\ Step 2: Alternatively, use the commutative property to rearrange terms: \97 + (-21)\ + (-97) = 97 + (-97) + (-21) Step 3: Simplify. 0 + (-21) = -21 The simplified value is -21. 6. Step 1: Calculate the combined earnings for the two weeks. Earnings last week = ₹4,200 Earnings this week = ₹10,800 Combined earnings = ₹4,200 + ₹10,800 = ₹15,000 Step 2: Determine if it's a profit or a loss. Since the shop earned money, it is a profit. The combined earnings for the two weeks are ₹15,000. It is a profit. 7. Step 1: Determine the initial height of the balloon. Initial height = +415 metres Step 2: Determine the change in height. Change in height = -120 metres (negative indicates a decrease in height) Step 3: Calculate the new height. New height = Initial height + Change in height 415 + (-120) = 415 - 120 = 295 metres Step 4: Determine if the balloon went up or came down. Since the new height (295 m) is less than the initial height (415 m), the balloon came down. Step 5: Explain why a hot-air balloon rises up. A hot-air balloon rises because the air inside the balloon is heated, making it less dense than the cooler air outside. This difference in density creates an upward buoyant force that lifts the balloon. The new height is 295 metres. The balloon came down from the initial height. A hot-air balloon rises because the air inside it is heated, making it less dense than the surrounding cooler air, which generates an upward buoyant force. What's next?

Accepted Answer · 2026-04-17T14:02:42.685Z

Right nishakumari81320412, let's go. Practice 1 1. Add: a) Step 1: Add -18 and 13. -18 + 13 = -5 The sum is -5. b) Step 1: Add 24 and -24. 24 + (-24) = 24 - 24 = 0 The sum is 0. c) Step 1: Add 65 and -25. 65 + (-25) = 65 - 25 = 40 The sum is 40. d) Step 1: Add 11 and 34. 11 + 34 = 45 The sum is 45. e) Step 1: Add -22 and -32. -22 + (-32) = -22 - 32 = -54 The sum is -54. 2. Add: a) Step 1: Add -102, -54, and -34. -102 + (-54) + (-34) = -102 - 54 - 34 = -156 - 34 = -190 The sum is -190. b) Step 1: Add 105, -92, and -7. 105 + (-92) + (-7) = 105 - 92 - 7 = 13 - 7 = 6 The sum is 6. c) Step 1: Add -52, -38, and -20. -52 + (-38) + (-20) = -52 - 38 - 20 = -90 - 20 = -110 The sum is -110. d) Step 1: Add 75, -23, and -45. 75 + (-23) + (-45) = 75 - 23 - 45 = 52 - 45 = 7 The sum is 7. 3. Fill in the blanks: a) Step 1: The equation is -16 + 29 = 29 + ____. Step 2: By the commutative property of addition, a+b = b+a. -16 + 29 = 29 + (-16) The blank is -16. b) Step 1: The equation is -54 + ____ = 0. Step 2: The sum of a number and its additive inverse is 0. -54 + 54 = 0 The blank is 54. c) Step 1: The equation is -25 + ____ = -25. Step 2: Adding 0 to any number does not change the number. -25 + 0 = -25 The blank is 0. d) Step 1: The equation is ____ + \41 + (-10)\ = -10. Step 2: Simplify the expression in the curly brackets. 41 + (-10) = 41 - 10 = 31 Step 3: The equation becomes ____ + 31 = -10. Step 4: Subtract 31 from both sides. ____ = -10 - 31 = -41 The blank is -41. e) Step 1: The equation is 36 + \-48 + ____\ = -48. Step 2: For the sum to be -48, the term \-48 + ____\ must be equal to -48 - 36 = -84. Step 3: So, -48 + ____ = -84. Step 4: Add 48 to both sides. ____ = -84 + 48 = -36 The blank is -36. f) Step 1: The equation is \24 + (-18)\ + ____ = -18. Step 2: Simplify the expression in the curly brackets. 24 + (-18) = 24 - 18 = 6 Step 3: The equation becomes 6 + ____ = -18. Step 4: Subtract 6 from both sides. ____ = -18 - 6 = -24 The blank is -24. g) Step 1: The equation is 30 + ____ = -24 + 30. Step 2: By the commutative property of addition, -24 + 30 = 30 + (-24). 30 + ____ = 30 + (-24) The blank is -24. 4. Add: a) Step 1: Find the additive inverse of -31. The additive inverse of -31 is 31. Step 2: Add -31 and its additive inverse 31. -31 + 31 = 0 The sum is 0. b) Step 1: Find the additive inverse of 44, which is -44. Step 2: Find the additive inverse of -10, which is 10. Step 3: Add these two additive inverses. -44 + 10 = -34 The sum is -34. 5. Simplify by applying commutative and associative properties: a) Step 1: Apply the associative property of addition: a + (b + c) = (a + b) + c. -32 + \32 + 75\ = (-32 + 32) + 75 Step 2: Simplify the expression in the parentheses. 0 + 75 = 75 The simplified value is 75. b) Step 1: Apply the associative property of addition: a + (b + c) = (a + b) + c. 65 + \80 + (-65)\ = (65 + (-65)) + 80 Step 2: Simplify the expression in the parentheses. 0 + 80 = 80 The simplified value is 80. c) Step 1: Apply the associative property of addition: (a + b) + c = a + (b + c). \112 + 50\ + (-112) = 112 + \50 + (-112)\ Step 2: Alternatively, use the commutative property to rearrange terms: \112 + 50\ + (-112) = 112 + (-112) + 50 Step 3: Simplify. 0 + 50 = 50 The simplified value is 50. d) Step 1: Apply the associative property of addition: (a + b) + c = a + (b + c). \97 + (-21)\ + (-97) = 97 + \(-21) + (-97)\ Step 2: Alternatively, use the commutative property to rearrange terms: \97 + (-21)\ + (-97) = 97 + (-97) + (-21) Step 3: Simplify. 0 + (-21) = -21 The simplified value is -21. 6. Step 1: Calculate the combined earnings for the two weeks. Earnings last week = ₹4,200 Earnings this week = ₹10,800 Combined earnings = ₹4,200 + ₹10,800 = ₹15,000 Step 2: Determine if it's a profit or a loss. Since the shop earned money, it is a profit. The combined earnings for the two weeks are ₹15,000. It is a profit. 7. Step 1: Determine the initial height of the balloon. Initial height = +415 metres Step 2: Determine the change in height. Change in height = -120 metres (negative indicates a decrease in height) Step 3: Calculate the new height. New height = Initial height + Change in height 415 + (-120) = 415 - 120 = 295 metres Step 4: Determine if the balloon went up or came down. Since the new height (295 m) is less than the initial height (415 m), the balloon came down. Step 5: Explain why a hot-air balloon rises up. A hot-air balloon rises because the air inside the balloon is heated, making it less dense than the cooler air outside. This difference in density creates an upward buoyant force that lifts the balloon. The new height is 295 metres. The balloon came down from the initial height. A hot-air balloon rises because the air inside it is heated, making it less dense than the surrounding cooler air, which generates an upward buoyant force. What's next?

Practice problems on adding integers, including sums of two integers, three integers, and using properties of addition like commutative and additive inverse.

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Practice problems on adding integers, including sums of two integers, three integers, and using properties of addition like commutative and additive inverse.

Need help with your own homework?

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