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Chapter 5: Adding and Subtracting Integers

Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.

Grade 7Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
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Chapter Overview

This chapter teaches Adding and Subtracting Integers with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.

Key Technical Terms

  • Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
  • Integer (a positive whole number, negative whole number, or zero)
  • Prime Number (a whole number greater than 1 with exactly two positive factors)
  • Mathematical Model (a mathematical representation of a real situation)
  • Estimate (a close approximation used to check whether an answer is reasonable)
  • Solution (a value or result that satisfies the problem)
  • Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
  • Reasonableness (whether an answer makes sense in the context of the problem)

How to Learn This Chapter

Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

5.1 Adding positive integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers .

Answer: 5

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Adding positive integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.2 Adding negative integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers .

Answer: 5

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Adding negative integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.3 Adding integers with different signs

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs .

Answer: 5

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Adding integers with different signs. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.4 Number-line addition

Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Number-line addition: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Number-line addition: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Number-line addition: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Number-line addition: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Number-line addition: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Explain Number-line addition in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Number-line addition becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Number-line addition and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Number-line addition becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Number-line addition using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Number-line addition becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Number-line addition problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Number-line addition becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Number-line addition could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Number-line addition becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Number-line addition. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.5 Counter models

The mode is the value that occurs most often. This topic focuses on Counter models .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Paint a room

  1. Model wall area and paint coverage
  2. State assumptions.
  3. Calculate using the model.
  4. Check whether the result is realistic.
  5. Revise if needed.

Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Counter models .

Answer: Estimate litres and cost

Worked Example 2

Problem: Tile a floor

  1. Model floor area and tile area
  2. State assumptions.
  3. Calculate using the model.
  4. Check whether the result is realistic.
  5. Revise if needed.

Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Counter models .

Answer: Estimate tile count plus waste

Worked Example 3

Problem: Plan a school event

  1. Model attendance and cost per person
  2. State assumptions.
  3. Calculate using the model.
  4. Check whether the result is realistic.
  5. Revise if needed.

Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Counter models .

Answer: Estimate total cost

Worked Example 4

Problem: Compare transportation

  1. Model fixed and per-kilometre costs
  2. State assumptions.
  3. Calculate using the model.
  4. Check whether the result is realistic.
  5. Revise if needed.

Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Counter models .

Answer: Find a break-even distance

Worked Example 5

Problem: Plan monthly savings

  1. Model starting savings plus monthly deposits
  2. State assumptions.
  3. Calculate using the model.
  4. Check whether the result is realistic.
  5. Revise if needed.

Very beginner explanation: The mode is the value that occurs most often. This topic focuses on Counter models .

Answer: Predict when a goal is reached

Worked Example 6

Problem: Tile a floor

  1. Write a simple rule: area = length × width.
  2. State any assumptions.
  3. Use the rule on sample values.
  4. Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Estimate tile quantity and include a small waste allowance.

Worked Example 7

Problem: Plan monthly savings

  1. Write a simple rule: total = starting amount + monthly deposit × months.
  2. State any assumptions.
  3. Use the rule on sample values.
  4. Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Predict when the savings goal is reached.

Worked Example 8

Problem: Simulate a die

  1. Write a simple rule: generate a random whole number from 1 to 6.
  2. State any assumptions.
  3. Use the rule on sample values.
  4. Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Repeat many times and compare frequencies.

Worked Example 9

Problem: Translate a point

  1. Write a simple rule: new x = x + 3; new y = y - 2.
  2. State any assumptions.
  3. Use the rule on sample values.
  4. Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Apply the same rule to every point.

Worked Example 10

Problem: Estimate paint needed

  1. Write a simple rule: paint = wall area ÷ coverage per can.
  2. State any assumptions.
  3. Use the rule on sample values.
  4. Check whether the result is realistic.

Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.

Answer: Round up because a partial can may not be enough.

Practice Exercise

Create one new question about Counter models. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.6 Subtracting positive integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. -7 + (-5) = -12.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Answer: -12

Worked Example 2

Problem: Calculate 4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. 4 + (9) = 13.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Answer: 13

Worked Example 3

Problem: Calculate -6 - (-3).

  1. Rewrite subtraction as adding the opposite.
  2. -6 + (3) = -3.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Answer: -3

Worked Example 4

Problem: Calculate 12 - (-8).

  1. Rewrite subtraction as adding the opposite.
  2. 12 + (8) = 20.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Answer: 20

Worked Example 5

Problem: Calculate -15 - (20).

  1. Rewrite subtraction as adding the opposite.
  2. -15 + (-20) = -35.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers .

Answer: -35

Worked Example 6

Problem: Calculate -8 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 5 is -5.
  3. Compute -8+(-5).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -13

Worked Example 7

Problem: Calculate 7 - (-12).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -12 is 12.
  3. Compute 7+(12).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 19

Worked Example 8

Problem: Calculate -4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -9 is 9.
  3. Compute -4+(9).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 5

Worked Example 9

Problem: Calculate 15 - (-6).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -6 is 6.
  3. Compute 15+(6).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 21

Worked Example 10

Problem: Calculate -20 - (13).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 13 is -13.
  3. Compute -20+(-13).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -33

Practice Exercise

Create one new question about Subtracting positive integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.7 Subtracting negative integers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. -7 + (-5) = -12.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Answer: -12

Worked Example 2

Problem: Calculate 4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. 4 + (9) = 13.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Answer: 13

Worked Example 3

Problem: Calculate -6 - (-3).

  1. Rewrite subtraction as adding the opposite.
  2. -6 + (3) = -3.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Answer: -3

Worked Example 4

Problem: Calculate 12 - (-8).

  1. Rewrite subtraction as adding the opposite.
  2. 12 + (8) = 20.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Answer: 20

Worked Example 5

Problem: Calculate -15 - (20).

  1. Rewrite subtraction as adding the opposite.
  2. -15 + (-20) = -35.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers .

Answer: -35

Worked Example 6

Problem: Calculate -8 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 5 is -5.
  3. Compute -8+(-5).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -13

Worked Example 7

Problem: Calculate 7 - (-12).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -12 is 12.
  3. Compute 7+(12).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 19

Worked Example 8

Problem: Calculate -4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -9 is 9.
  3. Compute -4+(9).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 5

Worked Example 9

Problem: Calculate 15 - (-6).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -6 is 6.
  3. Compute 15+(6).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 21

Worked Example 10

Problem: Calculate -20 - (13).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 13 is -13.
  3. Compute -20+(-13).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -33

Practice Exercise

Create one new question about Subtracting negative integers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.8 Adding the opposite

Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Adding the opposite: Identify a correct example.

  1. State the definition and show why the example fits.
  2. Show all important reasoning.

Very beginner explanation: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 2

Problem: Adding the opposite: Identify a non-example.

  1. Explain which requirement is missing.
  2. Show all important reasoning.

Very beginner explanation: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 3

Problem: Adding the opposite: Compare two cases.

  1. State one similarity and one difference.
  2. Show all important reasoning.

Very beginner explanation: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 4

Problem: Adding the opposite: Apply the idea in a real situation.

  1. Translate the situation into mathematical language.
  2. Show all important reasoning.

Very beginner explanation: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 5

Problem: Adding the opposite: Create and check your own example.

  1. Use the definition, then verify each condition.
  2. Show all important reasoning.

Very beginner explanation: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: A correct response must satisfy the definition or rule and include a check.

Worked Example 6

Problem: Calculate -8 - (5).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 5 is -5.
  3. Compute -8+(-5).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -13

Worked Example 7

Problem: Calculate 7 - (-12).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -12 is 12.
  3. Compute 7+(12).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 19

Worked Example 8

Problem: Calculate -4 - (-9).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -9 is 9.
  3. Compute -4+(9).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 5

Worked Example 9

Problem: Calculate 15 - (-6).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of -6 is 6.
  3. Compute 15+(6).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: 21

Worked Example 10

Problem: Calculate -20 - (13).

  1. Rewrite subtraction as adding the opposite.
  2. The opposite of 13 is -13.
  3. Compute -20+(-13).

Very beginner explanation: Subtracting an integer is equivalent to adding its opposite.

Answer: -33

Practice Exercise

Create one new question about Adding the opposite. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.9 Multi-step integer expressions

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Multi-step integer expressions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.10 Temperature-change problems

Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 5

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Temperature-change problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.11 Score-change problems

Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Answer: 5

Worked Example 6

Problem: Explain Score-change problems in one simple sentence.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Score-change problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: State the meaning, then give one small example.

Worked Example 7

Problem: Give one example that does not satisfy Score-change problems and explain why.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Score-change problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Identify the rule or condition that fails.

Worked Example 8

Problem: Show Score-change problems using a table, diagram, number line, graph, or equation.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Score-change problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Choose the representation that makes the relationship easiest to see.

Worked Example 9

Problem: After solving a Score-change problems problem, how can you check the answer?

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Score-change problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Use estimation, an inverse operation, substitution, or a second representation.

Worked Example 10

Problem: Give one real-life situation where Score-change problems could be useful.

  1. Read the definition of the topic.
  2. Use the definition to build the response.
  3. Check that the response matches every important condition.

Very beginner explanation: Score-change problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.

Answer: Connect the idea to money, measurement, data, design, or technology.

Practice Exercise

Create one new question about Score-change problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.12 Financial integer problems

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate -7 + (5).

  1. Use sign rules or a number line.
  2. The result is -2.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Answer: -2

Worked Example 2

Problem: Calculate 4 + (-9).

  1. Use sign rules or a number line.
  2. The result is -5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Answer: -5

Worked Example 3

Problem: Calculate -6 + (-3).

  1. Use sign rules or a number line.
  2. The result is -9.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Answer: -9

Worked Example 4

Problem: Calculate 12 + (-8).

  1. Use sign rules or a number line.
  2. The result is 4.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Answer: 4

Worked Example 5

Problem: Calculate -15 + (20).

  1. Use sign rules or a number line.
  2. The result is 5.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems .

Answer: 5

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Financial integer problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

5.13 Checking integer answers

An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Beginner Note

Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Place -7 on a number line.

  1. Start at 0.
  2. Move 7 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Answer: -7 is negative.

Worked Example 2

Problem: Place 4 on a number line.

  1. Start at 0.
  2. Move 4 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Answer: 4 is positive.

Worked Example 3

Problem: Place -6 on a number line.

  1. Start at 0.
  2. Move 6 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Answer: -6 is negative.

Worked Example 4

Problem: Place 12 on a number line.

  1. Start at 0.
  2. Move 12 units right.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Answer: 12 is positive.

Worked Example 5

Problem: Place -15 on a number line.

  1. Start at 0.
  2. Move 15 units left.

Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers .

Answer: -15 is negative.

Worked Example 6

Problem: Calculate -8 + (5).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -3

Worked Example 7

Problem: Calculate 7 + (-12).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -5

Worked Example 8

Problem: Calculate -4 + (-9).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -13

Worked Example 9

Problem: Calculate 15 + (-6).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: 9

Worked Example 10

Problem: Calculate -20 + (13).

  1. Use a number line or sign rules.
  2. If signs differ, subtract absolute values and keep the sign of the larger absolute value.

Very beginner explanation: Integer addition can be understood as movement left and right on a number line.

Answer: -7

Practice Exercise

Create one new question about Checking integer answers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.

Chapter Notes, Practice, and Common Mistakes

Chapter Notes

  • Read the complete question before choosing an operation, formula, graph, or model.
  • Write technical words together with their meaning until you are comfortable using them.
  • Show all important steps so another student can follow your reasoning.
  • Keep units, labels, signs, axes, variables, and mathematical symbols clear.
  • Estimate before or after calculating when an estimate can help check reasonableness.
  • For real-life problems, explain what the final number means in the situation.

Extra Practice

  1. Create and solve a new question about Adding positive integers . Show your reasoning and check your answer.
  2. Create and solve a new question about Adding negative integers . Show your reasoning and check your answer.
  3. Create and solve a new question about Adding integers with different signs . Show your reasoning and check your answer.
  4. Create and solve a new question about Number-line addition . Show your reasoning and check your answer.
  5. Create and solve a new question about Counter models . Show your reasoning and check your answer.
  6. Create and solve a new question about Subtracting positive integers . Show your reasoning and check your answer.
  7. Create and solve a new question about Subtracting negative integers . Show your reasoning and check your answer.
  8. Create and solve a new question about Adding the opposite . Show your reasoning and check your answer.
  9. Create and solve a new question about Multi-step integer expressions . Show your reasoning and check your answer.
  10. Create and solve a new question about Temperature-change problems . Show your reasoning and check your answer.
  11. Create and solve a new question about Score-change problems . Show your reasoning and check your answer.
  12. Create and solve a new question about Financial integer problems . Show your reasoning and check your answer.

Common Mistakes

  • Ignoring place value or signs.
  • Using an operation before checking what the question asks.
  • Skipping estimation and accepting an unreasonable result.
  • Forgetting the correct order of operations.
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30 Review Questions and Answers

Q1. What is important to remember about Adding positive integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding positive integers.

Q2. What is important to remember about Adding negative integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding negative integers.

Q3. What is important to remember about Adding integers with different signs?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Adding integers with different signs.

Q4. What is important to remember about Number-line addition?

Answer: Number-line addition is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Counter models?

Answer: The mode is the value that occurs most often. This topic focuses on Counter models.

Q6. What is important to remember about Subtracting positive integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting positive integers.

Q7. What is important to remember about Subtracting negative integers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Subtracting negative integers.

Q8. What is important to remember about Adding the opposite?

Answer: Adding the opposite is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Multi-step integer expressions?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Multi-step integer expressions.

Q10. What is important to remember about Temperature-change problems?

Answer: Temperature-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q11. What is important to remember about Score-change problems?

Answer: Score-change problems is an important Grade 7 idea in Adding and Subtracting Integers. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Financial integer problems?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Financial integer problems.

Q13. What is important to remember about Checking integer answers?

Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Checking integer answers.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer you obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.

Q26. How should you study this chapter?

Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.

Q27. When is a calculator useful?

Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.

Q28. Why compare more than one strategy?

Answer: Different strategies can make a problem easier and provide a way to verify the result.

Q29. What is a mathematical model?

Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.

Q30. Why should assumptions be stated?

Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.