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.
• Symbols for Multiplication:

1. $\mathbf{×}$,  like the letter "x" . e.g.

2. $·$ , a dot, E.g.

3. $\left(\right)\left(\right)$, no symbol between parentheses,  e.g.

• Symbols for Division:

1.   ; e.g.

2.  A long division sign

3.  A fraction sign; e.g. $\frac{3}{5}$

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: $\left(-7\right)\left(-9\right)$

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

Example 2: Find the product: $-3·4$

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

Example 3: Solve: $\left(4\right)\left(-8\right)$

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

Example 4: Divide:

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

Example 5: Solve:$\frac{36}{-6}$

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

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.

, follow the rule of multiplying integers with the same sign.

, follow the rule of subtraction of integers with the same sign.