Multiplication and Division

MULTIPLICATION AND DIVISION FACTS

Multiplication Basics

What is multiplication?

Multiplication is when you take one number and add it together with a number of times.

Example:

5 multiplied by 4 = 5 + 5 + 5 + 5 = 20

We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

More examples:

7 x 3 = 7 + 7 + 7 = 21
2 x 1 = 2
3 x 6 = 3 + 3 + 3 + 3 + 3 + 3 = 18

Signs for Multiplication

There are a few different signs that people use to indicate multiplication. The most common is the "x" sign, but sometimes people use a "*" sign or other symbols. Here are some ways to indicate 5 multiplied by 4.

5 x 4
5 * 4
5 times 4

Sometimes when people use variables in multiplication they will just put the variables next to each other to indicate multiplication. Here are a few examples:

ab = a x b
(a +1)(b + 1) = (a +1) x (b + 1)

Factors and Products

Sometimes when teachers talk about multiplication they will use the terms factors and products.

Factors are the numbers you are multiplying together. Products are the answers.

(factor) x (factor) = product

Multiplying by Zero and One

Zero and one are two special cases when multiplying.

When multiplying by 0, the answer is always 0.

Examples:

1 x 0 = 0
7676 x 0 = 0
0 x 12 = 0
0 x b = 0

When multiplying by 1, the answer is always the same as the number multiplied by 1.

Examples:

1 x 12 = 12
7654 x 1 = 7654
1 x 0 = 0
1 x b = b

Order Doesn't Matter

An important rule to remember with multiplication is that the order you multiply numbers doesn't matter. You can multiply them in any order you want and the answer will be the same. This can help sometimes when you get stuck on a problem. Just try it the other way.

Examples:

5 x 4 = 4 + 4 + 4 + 4 + 4 = 20
4 x 5 = 5 + 5 + 5 + 5 = 20
3 x 2 = 2 + 2 + 2 = 6
2 x 3 = 3 + 3 = 6
4 x 1 = 1 + 1 + 1 +1 = 4
1 x 4 = 4 = 4

Multiplication Table

Once you learn the basics of multiplication, you will want to learn the multiplication table, also called the times' table. This table includes all of the possible multiplications between the numbers 1 to 12. That is all the way from 1 x 1 to 12 x 12.

It may sound like a lot of useless work to memorize this table, but it will help you a LOT later in school. You will be able to solve harder problems faster and easier if you know these numbers by heart.

Here is the table:
https://www.ducksters.com/kidsmath/times_table_lg.jpg

MULTIPLICATION

DIVISION

What is division?

Division is breaking a number up into an equal number of parts.

Example:

20 divided by 4 = ?

If you take 20 things and put them into four equal sized groups, there will be 5 things in each group. The answer is 5.

20 divided by 4 = 5.

Signs for Division

There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction.

Example signs for "a divided by b":

a ÷ b
a/b
a
b

Dividend, Divisor, and Quotient

Each part of a division equation has a name. The three main names are the dividend, the divisor, and the quotient.

Dividend - The dividend is the number you are dividing up
Divisor - The divisor is the number you are dividing by
Quotient - The quotient is the answer

Dividend ÷ Divisor = Quotient

Example:

In the problem 20 ÷ 4 = 5

Dividend = 20
Divisor = 4
Quotient = 5

Special Cases

There are three special cases to consider when dividing.

1) Dividing by 1: When dividing something by 1, the answer is the original number. In other words, if the divisor is 1 then the quotient equals the dividend.

Examples:

20 ÷ 1 = 20
14.7 ÷ 1 = 14.7

2) Dividing by 0: You cannot divide a number by 0. The answer to this question is undefined.

3) Dividend equals Divisor: If the dividend and the divisor are the same number (and not 0), then the answer is always 1.

Examples:

20 ÷ 20 = 1
14.7 ÷ 14.7 = 1

Remainder

If the answer to a division problem is not a whole number, the "leftovers" are called the remainder.

For example, if you were to try and divide 20 by 3 you would discover that 3 does not divide evenly into 20. The closest numbers to 20 that 3 can divide into are 18 and 21. You pick the closest number that 3 divides into that is smaller than 20. That is 18.

18 divided by 3 = 6, but there are still some leftovers. 20 -18 = 2. There are 2 remaining.

We write the remainder after an "r" in the answer.

20 ÷ 3 = 6 r 2

Examples:

12 ÷ 5 = 2 r 2
23 ÷ 4 = 5 r 3
18 ÷ 7 = 2 r 4

Division is the Opposite of Multiplication

Another way to think of division is as the opposite of multiplication. Taking the first example on this page:

20 ÷ 4 = 5

You can do the reverse, replacing the = with a x sign and the ÷ with an equal sign:

5 x 4 = 20

Examples:

12 ÷ 4 = 3
3 x 4 = 12

21 ÷ 3 = 7
7 x 3 = 21

Using multiplication is a great way to check your division work and get better scores on your math tests!