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Lesson 18 of 19

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Fourteen ideas, fourteen questions. The table is here if you need to look back.

Operations with Integers — fourteen moves
MoveHow it goes
Add, same sideAdd the sizes. Keep that side. (−3) + (−4) = −7.
Add, mixed sidesBigger size wins the side. Subtract to find the distance.
Take awaya − b is a + (−b). One rule instead of two.
Take away below zeroThe walk turns right. 5 − (−3) = 8.
In your headRewrite as an add, compare sizes, then pick the side.
MultiplyOne move, repeated. (−3) × 4 is 12 left, so −12.
Multiply, both belowNo zero factor? Same sign gives more than zero. Different signs, less.
ShareSame sign rule as multiply, since share undoes it.
ZeroTimes zero is zero. Adding zero changes nothing. ÷ 0: no answer.
A changeLater reading take away earlier. The side says which way.
Zero pairsA zero pair is one positive and one negative token. To take away tokens you lack, add zero pairs first.
Additive inverseAdding a number to its additive inverse gives 0. For a, that partner is written −a. Multiplying by −1 finds the partner.
Many factorsNo zero among the factors? Count the negative ones. An even count gives a product more than zero. An odd count gives a product less than zero. A zero factor makes the product 0.
A bracketMultiply the number by each part of the bracket, then add. The answer matches adding the bracket first. It still holds when a number is below zero.

A quiz team loses 4 points, then loses 5 more. Where does its score stand?

  • On 9, because two losses cancel out
  • On −1, because 5 take away 4 is 1
  • On −9

What is 7 + (−11)?

  • −4
  • 18
  • 4

Which of these means exactly the same as (−8) − 3?

  • (−8) + 3
  • (−8) + (−3)
  • 8 − 3

A lift is on level 1. The parking below is level −2. How many levels apart are they?

  • 1, because 2 take away 1 is 1
  • −1
  • 3

Without drawing anything, which side of zero does (−9) + 4 land on?

  • Left of zero
  • Right of zero
  • Exactly on zero

What does (−6) × 3 come to?

  • −3, because 6 take away 3 is 3
  • −18
  • 18

The −5 times table reads −10, −5, 0. The count drops 2, 1, 0. What is (−5) × (−1)?

  • −5, because the pattern repeats
  • 0, because the table has run out
  • 5

What is (−3) + (−4), and what is (−3) × (−4)?

  • The sum is −7 and the product is 12
  • The sum is 7 and the product is 12
  • The sum is −7 and the product is −12

What is (−24) ÷ (−6)?

  • −4
  • 4
  • −144

A thermometer read −6 °C at dawn and −1 °C at nine. What was the change, and which way?

  • 5, and it went up
  • −5, and it went down
  • 7, and it went up

A bag holds 2 positive tokens. How do you work out 2 − 7 with tokens?

  • Take away 7 positive tokens straight away
  • Add 2 zero pairs, then take away 7 positive tokens
  • Add 5 zero pairs, then take away 7 positive tokens

Find the additive inverse of −13. What do the two add up to?

  • 13, and they add up to 0
  • −13, and they add up to −26
  • 13, and they add up to 26

Without multiplying, which side of zero is (−3) × 2 × (−4) × (−1) × 5?

  • More than zero
  • Less than zero
  • Exactly zero

Which line equals (−5) × (3 + (−2))?

  • (−5) × 3 + (−2)
  • (−5) × 3 + 5 × (−2)
  • (−5) × 3 + (−5) × (−2)

Part II, Chapter 2 is Operations with Integers. Look for these ideas in it.

Next: Finding Common Ground — the factors and multiples two numbers share.

Reveal every answer to finish this lesson.