6th Grade - Multiplying and Dividing Integers

Introduction

  • Integers are a set of whole numbers (0, 1, 2, 3, ....) and their opposites. For example, 1, -1,  2, -2, 3, -3, and so on.
  • 0 is an integer. It is also called the origin. 0 does not carry any sign. When any integer is multiplied by 0, the answer is always 0. e.g. -5 × 0 = 0
  • Symbols for Multiplication:

1. ×,  like the letter "x" . e.g. -3 × 2 = -6

2. · , a dot, E.g. -3·2 = -6

3. , no symbol between parentheses,  e.g. -45 = -20

  • Symbols for Division:

1.   ÷ ; e.g. 12 ÷ 3

2.  A long division sign

3.  A fraction sign; e.g. 35

Multiplying and Dividing Integers

  • Rule 1: When multiplying or dividing two integers with the same sign, multiply/divide the integers and give the result a positive sign.

(+) × (+) = (+)

(-) × (-) = (+)

(+) ÷ (+) = (+)

(-) ÷ (-) = (+)

  • Rule 2: When multiplying or dividing two integers with different signs, multiply/divide the integers and give the result a negative sign.

(+) × (-) = (-)

(-) × (+) = (-)

(+) ÷  (-) = (-)

(-) ÷ (+) = (-)

  • Follow the order of operations when multiplying and dividing more than two integers.

Solved Examples

Example 1: Multiply: -7-9

Solution: Follow the rules of multiplying integers with the same sign.

-7 × -9= 63

 

Example 2: Find the product: -3·4

Solution: Follow the rule of multiplying integers with different signs.

-3 · 4 = -12

 

Example 3: Solve: 4-8

Solution: Follow the rule of multiplying integers with different signs.

= 4 × -8

= -32

 

Example 4: Divide: -36 ÷ -9

Solution: Follow the rule of dividing integers with the same sign.

-36 ÷ -9 = 4

 

Example 5: Solve:36-6

Solution: Follow the rule of dividing integers with different signs.

36-6 = -6

Cheat Sheet

  • Multiplying or dividing integers with the same sign:

Positive x Positive = Positive

Negative x Negative = Positive

Positive ÷ Positive = Positive

Negative ÷ Negative = Positive

  • Multiplying or dividing integers with different signs:

Positive x Negative = Negative

Negative x Positive = Negative

Positive ÷ Negative = Negative

Negative ÷ Positive = Negative

Blunder Areas

  • When multiplying or dividing integers, follow the rules of multiplying and dividing integers. Do not get confused with the rules of addition or subtraction of integers.
  • Do not misinterpret parentheses. E.g. -3(-2)  -3 -2

-3-2 = 6, follow the rule of multiplying integers with the same sign.

-3-2 =-5, follow the rule of subtraction of integers with the same sign.