Year 7 NSW Maths Integers Worksheet | Add and Subtract Integers

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Instructions

Building on what we learned about comparing, ordering, and calculating with integers, this worksheet introduces order of operations with integers. You will learn how to calculate expressions with brackets and more than one operation.

  1. Complete the review questions first.
  2. Read the order-of-operations rules carefully.
  3. Show each step of your working.
  4. Remember that negative numbers are integers too.
  5. Complete the challenge if you are ready for a harder problem.

Learning Goals

  • Review integer comparisons and calculations.
  • Use brackets to group operations.
  • Apply the order of operations to integer expressions.
  • Work from left to right when multiplication and division, or addition and subtraction, have equal priority.
  • Solve real-world problems using multi-step integer expressions.

Mission 1: Integer Skills Warm-Up

A. Compare and order

  1. Write >, <, or = in each box.

    • -7 [ ] -2
    • 4 [ ] -4
    • -10 [ ] -10
    • 0 [ ] -6

  2. Order these integers from least to greatest:

    • 6, -3, 0, -9, 2

    Answer: __

B. Calculate

  1. Calculate each expression.

    • -8 + 13 = __
    • 7 - 15 = __
    • -6 - (-9) = __
    • (-4) × (-5) = __
    • 42 ÷ (-7) = __

C. Real-world review

  1. The temperature is -6°C. It rises by 11°C. What is the new temperature?

    Working: __

    Answer: __

Mission 2: Discover the Order of Operations

When an expression has more than one operation, use this order:

  1. Calculate inside brackets first.
  2. Calculate multiplication and division from left to right.
  3. Calculate addition and subtraction from left to right.

Worked examples

  • 7 + 3 × (-2)

  • Multiplication first: 3 × (-2) = -6

  • Then add: 7 + (-6) = 1

  • Answer: 1

  • [8 + (-5)] × 4

  • Brackets first: 8 + (-5) = 3

  • Then multiply: 3 × 4 = 12

  • Answer: 12

Try the steps

For each expression, circle or underline the operation you should complete first. Then calculate.

  1. 6 + 4 × (-3)

    First operation: ____

    Answer: __

  2. (-18 ÷ 3) + 5

    First operation: ____

    Answer: __

  3. 12 - [4 + (-7)]

    First operation: ____

    Answer: __

  4. (-5) × [2 - 6]

    First operation: ____

    Answer: __

  5. 18 ÷ [(-3) + 6]

    First operation: ____

    Answer: __

Mission 3: Step-by-Step Integer Expressions

Building on your integer-operation skills, now solve expressions with several operations. Write at least one intermediate step for every question.

  1. 9 - 2 × (-4)

    Working: __

    Answer: __

  2. [(-6) + 10] × (-3)

    Working: __

    Answer: __

  3. 24 ÷ (-6) - 7

    Working: __

    Answer: __

  4. -3 × [5 + (-2)]

    Working: __

    Answer: __

  5. [(-8) - 4] ÷ (-3)

    Working: __

    Answer: __

  6. 20 - [6 × (-2) + 5]

    Working: __

    Answer: __

Helpful hint

Do not automatically work from left to right for the whole expression. Brackets and multiplication or division may need to be completed before addition or subtraction.

Mission 4: Which Calculation Comes First?

Write the number of the step that should be completed first. Then calculate the expression.

  1. -4 + 6 × 2

    First step: __

    Answer: __

  2. [(-9) + 3] ÷ 2

    First step: __

    Answer: __

  3. 15 - 20 ÷ (-5)

    First step: __

    Answer: __

  4. (-2) × 3 + 4 × (-1)

    First step: __

    Answer: __

  5. 30 ÷ [2 + (-7)]

    First step: __

    Answer: __

Mission 5: Real-World Integer Missions

Write an expression before calculating. Use brackets when they help show the groups of operations.

  1. A quiz score starts at -2 points. Mia answers 3 questions correctly and earns 5 points for each correct answer. What is her final score?

    Expression: __

    Working: __

    Answer: __

  2. A bank account contains $20. A payment of $8 is made, followed by a fee of $6. Represent the final balance as an integer.

    Expression: __

    Working: __

    Answer: __

  3. A lift is at level -1. It rises 4 levels twice. Which level does it reach?

    Expression: __

    Working: __

    Answer: __

  4. The temperature is -3°C. It drops by 4°C, then rises by 10°C. What is the final temperature?

    Expression: __

    Working: __

    Answer: __

  5. A diver is at -5 metres. She descends 3 metres, then rises 2 metres. What is her final position?

    Expression: __

    Working: __

    Answer: __

Mission 6: Complete the Organizer

The first row shows an example. For each new situation, write an integer expression, identify the first operation, and calculate the answer.

Situation Integer expression First operation Answer and meaning
A score of -4 gains 3 points twice -4 + 2 × 3 Multiplication: 2 × 3 2 points; the final score is 2
A temperature of -8°C rises 5°C, then drops 2°C
A bank balance of $12 loses $7 and then $4
A lift at level -3 rises 2 levels three times
A diver at -20 m rises 6 m, then descends 4 m
A game score of 5 loses 3 points twice

Mission 7: Explain Your Thinking

Answer in complete sentences.

  1. Why must you calculate 3 × (-4) before adding 7 in the expression 7 + 3 × (-4)?

  2. How do brackets change the calculation in these two expressions?

    • 6 + 2 × 5 = ______
    • (6 + 2) × 5 = ______

    Explain the difference:

  3. Write two different integer expressions that have an answer of -10. At least one must include brackets.

Optional Challenge: The Underground Expedition

A research team begins at an elevation of 40 metres. They descend 3 tunnels of 25 metres each, climb 18 metres, and then descend another 12 metres.

  1. Write one expression for the team’s journey.

  2. What is the team’s final elevation?

    Working: _____

    Answer: __

  3. What is the lowest elevation reached during the journey?

    Working: _____

    Answer: __

  4. How many metres lower is the final elevation than the starting elevation?

    Answer: __

Reflection

Complete the sentences.

  • One rule about order of operations that I can remember is __.
  • Brackets are useful because ____.
  • One expression I found challenging was __.
  • I can use multi-step integer calculations when ____.

Answer Key

Mission 1

A. Compare and order

1.

  • -7 < -2
  • 4 > -4
  • -10 = -10
  • 0 > -6
  1. -9, -3, 0, 2, 6

B. Calculate

3.

  • -8 + 13 = 5
  • 7 - 15 = -8
  • -6 - (-9) = 3
  • (-4) × (-5) = 20
  • 42 ÷ (-7) = -6

C. Real-world review

  1. -6 + 11 = 5; the new temperature is 5°C.

Mission 2

  1. Multiplication first: 4 × (-3) = -12; 6 + (-12) = -6. Answer: -6.
  2. Division first: -18 ÷ 3 = -6; -6 + 5 = -1. Answer: -1.
  3. Brackets first: 4 + (-7) = -3; 12 - (-3) = 15. Answer: 15.
  4. Brackets first: 2 - 6 = -4; (-5) × (-4) = 20. Answer: 20.
  5. Brackets first: (-3) + 6 = 3; 18 ÷ 3 = 6. Answer: 6.

Mission 3

  1. 9 - 2 × (-4) = 9 - (-8) = 17.
  2. [(-6) + 10] × (-3) = 4 × (-3) = -12.
  3. 24 ÷ (-6) - 7 = -4 - 7 = -11.
  4. -3 × [5 + (-2)] = -3 × 3 = -9.
  5. [(-8) - 4] ÷ (-3) = -12 ÷ (-3) = 4.
  6. 20 - [6 × (-2) + 5] = 20 - [-12 + 5] = 20 - (-7) = 27.

Mission 4

  1. First step: 6 × 2; -4 + 12 = 8. Answer: 8.
  2. First step: (-9) + 3; -6 ÷ 2 = -3. Answer: -3.
  3. First step: 20 ÷ (-5); 15 - (-4) = 19. Answer: 19.
  4. Multiplications are completed first. (-2) × 3 = -6 and 4 × (-1) = -4; -6 + (-4) = -10. Answer: -10.
  5. First step: 2 + (-7) = -5; 30 ÷ (-5) = -6. Answer: -6.

Mission 5

  1. Expression: -2 + 3 × 5. Calculation: -2 + 15 = 13. Mia’s final score is 13 points.
  2. Expression: 20 - 8 - 6, or 20 - [8 + 6]. Calculation: 20 - 14 = 6. The final balance is $6.
  3. Expression: -1 + 2 × 4. Calculation: -1 + 8 = 7. The lift reaches level 7.
  4. Expression: -3 - 4 + 10. Calculation: -7 + 10 = 3. The final temperature is 3°C.
  5. Expression: -5 - 3 + 2. Calculation: -8 + 2 = -6. The diver is at -6 metres.

Mission 6

Situation Integer expression First operation Answer and meaning
A score of -4 gains 3 points twice -4 + 2 × 3 Multiplication: 2 × 3 2 points; the final score is 2
A temperature of -8°C rises 5°C, then drops 2°C -8 + 5 - 2 Addition: -8 + 5 -5°C; the final temperature is -5°C
A bank balance of $12 loses $7 and then $4 12 - 7 - 4 Subtraction: 12 - 7 $1; the final balance is $1
A lift at level -3 rises 2 levels three times -3 + 3 × 2 Multiplication: 3 × 2 Level 3; the lift reaches level 3
A diver at -20 m rises 6 m, then descends 4 m -20 + 6 - 4 Addition: -20 + 6 -18 m; the diver is 18 m below sea level
A game score of 5 loses 3 points twice 5 - 2 × 3 Multiplication: 2 × 3 -1 point; the final score is -1

Mission 7

  1. Multiplication has priority over addition, so 3 × (-4) must be calculated first. The expression becomes 7 + (-12) = -5.
  2. 6 + 2 × 5 = 16; (6 + 2) × 5 = 40. In the first expression, multiplication happens first. In the second expression, brackets make the addition happen first.

  3. Answers will vary. Examples include:

    • -2 × 5 = -10
    • [4 - 9] × 2 = -10

Optional Challenge

  1. Expression: 40 - 3 × 25 + 18 - 12.
  2. 40 - 75 + 18 - 12 = -29; the final elevation is -29 metres.
  3. After descending 75 metres, the team is at -35 metres. After climbing 18 metres, it is at -17 metres. After descending 12 metres, it reaches -29 metres. The lowest elevation is -35 metres.
  4. 40 - (-29) = 69; the final elevation is 69 metres lower than the starting elevation.

Reflection answers will vary. Look for accurate use of the order-of-operations rules and a sensible real-world example.

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