Multiplying and dividing signed numbers

About this lesson

Grade 7 › Rational number arithmetic

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Multiplying and dividing signed numbers

Warm-up

Three quick questions from earlier lessons.

Discover

A tank loses 3 liters every minute (a change of −3-3 per minute). What was the change over the last 4 minutes?

  1. −12-12 liters
  2. 1212 liters

Key idea

Signs for products and quotients.

Same signs give a positive product or quotient; different signs give a negative one. (−a)(−b)=ab(-a)(-b) = ab, (−a)⋅b=−ab(-a) \cdot b = -ab, and division follows the same rules.

Worked example

(−6)(−5)÷(−3)(-6)(-5) \div (-3).

(−6)(−5)=30(-6)(-5) = 30
Same signs.
30÷(−3)=−1030 \div (-3) = -10
Different signs.

Your turn, guided

Your turn: (−48)÷(−6)(-48) \div (-6).

88
Same signs.

Practice ★

  1. Compute (−6)⋅7(-6) \cdot 7.
  2. Compute (−7)⋅11(-7) \cdot 11.
  1. Compute (−4)⋅(−6)(-4) \cdot (-6).

Watch out!

Practice ★★

  1. Compute (−144)÷12(-144) \div 12.
  2. Compute (−120)÷12(-120) \div 12.
  1. Boss problem. At midnight it is 5 °C. The temperature changes by −6-6 °C every hour (it drops 6 degrees per hour).

Exit ticket

Three questions to check you have got it.

  1. Compute (−6)⋅7(-6) \cdot 7.
  2. Compute (−7)⋅11(-7) \cdot 11.
  3. Compute (−11)⋅10(-11) \cdot 10.

Summary card

Multiplying and dividing signed numbers

Same signs: positive. Different signs: negative.

Watch out: negative times negative is positive.

End of the lesson

Next lesson: Solve linear equations in one variable Back to the chapter

Answers: Multiplying and dividing signed numbers

A

  1. −42-42
  2. −77-77

B

  1. 2424

C

  1. −12-12
  2. −10-10

D

  1. 1717

E

  1. −42-42
  2. −77-77
  3. −110-110

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