Multiplication

Background

We can add, but oftentimes we want to add the same number over and over again. Is there a way to do that?

Question

What is 2 x 6? 2 x 1? 2 x 0? 

Answer

2 x 6 = 12, 2 x 1 = 2, 2 x 0 = 0

Analysis

Sometimes we want to add the same number over and over again. Multiplication allows us to do a lot of additions all at once.

As a simple example, think of an ice tray that has 2 rows of 6 "pockets" each. How many pockets are in the tray? (Here's a picture that might help...)



We could count them individually (and often we'll point as we count each one to help keep track of what we've counted and what we haven't) and it'll take a second but we'll find 12 pockets are in the ice tray.

We could also see that there are 2 black pockets, 2 blue, 2 green, and so on. So we can add:

2 + 2 + 2 + 2 + 2 + 2 = 12

We could also count going the other way - we could see that there are 6 pockets of different colours in a row and there are 2 rows of them, so we could add up going the other way:

6 + 6 = 12

And lastly, we can use multiplication - it tells us that we have a number (say 2) and we want to add it up 6 times:

2 x 6 = 12

We can also see multiplication using the number line. If we look at 2 X 6, we want to start at 0 and then do +2 six times:



Let's now look at 2 x 1. The 1 is called the multiplicative identity. Just like how 0 is the additive identity, where we can add 0 as much as we want to a number and get that number again (2 + 0 = 2), the same works for 1 and multiplication:

2 x 1 x 1 x 1 x 1 = 2

And how about 2 x 0? Let's look at the number line - we start at 0 and we move up the number line in jumps of 2. We do that 0 times... which means we don't actually move, do we? Or put another way, if we say 0 x 2, we move 0 spots twice... or in other words, we don't actually move at all.

Any number multiplied by 0 equals 0.

Multiplication vocabulary! The first number is called the multiplicand. The second number is the multiplier. And the result of multiplication is called the product (and of the three terms, "product" is the term I most often hear).

Multiplication can be indicated in a number of ways. We can show 2 times 6 these ways:

2 x 6 = 12
2(6) = 12
(2)(6) = 12
2 * 6 = 12


Vocabulary used:

For more information check out these links (comment to add your favourite link):

http://studyjams.scholastic.com/studyjams/jams/math/multiplication-division/multiplication.htm

Where might you have come from?

Fact-orials Index

Numbers:

• The Number 1
• The Number 0
• Negative Numbers

Operations

• Addition

Where might we go?

Numbers:

• Prime and Composite Numbers

Operations:

• Division
• Exponentials
• Grouping Terms, Parentheses
• Order of Operations (PEMDAS)

Operations with different kinds of numbers:

• Multiplication, Division, and Whole Numbers
• Multiplication Table
• Multiplication, Division, and Integers
• Multiplication, Division, and Rational Numbers
• Addition, Subtraction, and Variables

Associated Operations:

• Factors and Factoring
• Multiples

Properties:

• Commutative Property
• Associative Property
• Distributive Property

Relations:

• Inverse Relations

Combinatorics:

• Factorials