Multiplying and Dividing Integers: A Simple Lesson!

Lesson Overview

• What Are Integers?
• Multiplication of Integers: How to Multiply Integers 
• Division of Integers
• Multiplication and Division of Integers Examples

Integers are like the building blocks of math, including positive numbers, negative numbers, and zero. In this lesson, learn how to multiply and divide these integers, opening up a whole new world of problem-solving.

What Are Integers?

Imagine a number line stretching out in both directions. You have zero in the middle, and then numbers like 1, 2, 3 going to the right. But what about the numbers going to the left? Those are integers too!

Example: 

• Positive integers are to the right of zero. ➡
• Negative integers are to the left of zero. ⬅
• Zero is in the middle. 

Take the Quiz :

Multiplying and Dividing Integers MCQ Quiz!

Multiplication of Integers: How to Multiply Integers 

Multiplication is like adding a number over and over again. Well, that still holds true with integers, but you need a few extra rules to handle those negative numbers.

Rules of Multiplication of Integers

For Example: 

• Rule 1: Positive ✖ Positive = Positive
  • 5 x 2 = 10
  • Getting 5 candies from your friend two days in a row. You gain candies! (5 candies + 5 candies = 10 candies)
    
• Rule 2: Negative ✖ Negative = Positive
  • -3 x -4 = 12
  • Taking away 3 debts for $4 from your friend. You are essentially giving your friend $12! (-3 x -$4 = $12)
    
• Rule 3: Positive ✖ Negative = Negative
  • 4 x -3 = -12
  • Losing 4 points in a game 3 times. Your score goes down! (-4 points + -4 points + -4 points = -12 points)
    
• Rule 4: Negative ✖ Positive = Negative
  • -2 x 5 = -10
  • Owing 2 candies to 5 friends. You have a total debt of 10 candies! (-2 candies + -2 candies + -2 candies + -2 candies + -2 candies = -10 candies)

Take the Quiz :

Multiplying and Dividing Negative Numbers.

Division of Integers

As multiplication is like repeated addition. Well, division is like repeated subtraction! It's all about splitting things into equal groups. 

Rules of Division Integers

For Example:

• Rule 1: Positive ÷ Positive = Positive
  • 10 ÷ 2 = 5. 
  • Imagine you have 10 cookies and want to share them equally with 2 friends. Each friend gets 5 cookies!
    
• Rule 2: Negative ÷ Negative = Positive
  • -12 ÷ -3 = 4. 
  • Imagine you owe $12 to 3 friends.  You owe each friend $4.  (-$12 shared among 3 friends = -$4 each)
    
• Rule 3: Positive ÷ Negative = Negative
  • 8 ÷ -4 = -2. 
  • Imagine you have 8 balloons and you want to divide them into groups of -4. This doesn't really make sense in the real world, but in math, it means each group would represent owing 2 balloons!
    
• Rule 4: Negative ÷ Positive = Negative
  • -15 ÷ 3 = -5. 
  • Imagine you owe $15 and want to split the debt equally among 3 friends. Each friend would owe $5.
    

Multiplication and Division of Integers Examples

Example 1: Saving Money

Imagine you save $5 every week. How much money will you have saved after 4 weeks?

• This is a positive x positive situation.
• We can write this as 5 x 4 = 20
• You will have saved $20!
  

Example 2: Sharing Candy

You have 12 pieces of candy and want to share them equally with 3 friends. How many pieces will each friend get?

• This is a positive ÷ positive situation.
• We can write this as 12 ÷ 3 = 4
• Each friend will get 4 pieces of candy.
  

Example 3: Losing Points in a Game

In a video game, you lose 3 points every time you hit an obstacle. If you hit 5 obstacles, how many points will you lose in total?

• This is a negative x positive situation.
• We can write this as -3 x 5 = -15
• You will lose 15 points.
  

Example 4: Distributing Debt

You and your two friends owe $15 to a store. If you split the debt equally, how much does each person owe?

• This is a negative ÷ positive situation.
• We can write this as -15 ÷ 3 = -5
• Each person owes $5.
  

Example 5: Going Downstairs

You go down 2 floors in a building every time you press the "down" button on the elevator. If you press the button 6 times, how many floors will you go down in total?

• This is a negative x positive situation.
• We can write this as -2 x 6 = -12
• You will go down 12 floors.