Adding and subtracting signed numbers

About this lesson

Grade 7 › Rational number arithmetic

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Adding and subtracting signed numbers

Discover

It is −3-3 °C and the temperature rises 5 degrees. What is it now?

  1. 22 °C
  2. −8-8 °C

Key idea

Add by moving on the number line; subtract by adding the opposite.

Adding a positive number moves right; adding a negative moves left. With different signs, subtract the sizes and keep the sign of the larger one. Subtracting is adding the opposite: a−b=a+(−b)a - b = a + (-b), so a−(−b)=a+ba - (-b) = a + b.

Worked example

−4−(−9)-4 - (-9).

−4+9-4 + 9
Add the opposite.
55
Different signs: 9 − 4, sign of 9.

Your turn, guided

Your turn: −6+(−7)-6 + (-7).

−13-13
Both left.

Practice ★

  1. Compute 7+(−16)7 + (-16).
  2. Compute 9+(−20)9 + (-20).
  1. Compute −9−10-9 - 10.

Watch out!

Practice ★★

  1. Compute 2−(−5)2 - (-5).
  2. Compute 8−(−5)8 - (-5).

Exit ticket

Three questions to check you have got it.

  1. Compute 7+(−16)7 + (-16).
  2. Compute 9+(−20)9 + (-20).
  3. Compute 8+(−15)8 + (-15).

Summary card

Adding and subtracting signed numbers

Move on the number line; subtract = add the opposite.

Watch out: minus a negative is plus.

End of the lesson

Next lesson: Multiplying and dividing signed numbers Back to the chapter

Answers: Adding and subtracting signed numbers

A

  1. −9-9
  2. −11-11

B

  1. −19-19

C

  1. 77
  2. 1313

D

  1. −9-9
  2. −11-11
  3. −7-7

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