Understanding Multiplication and Division Tutorial

What is multiplication?

4 x 3 = 12

This reads 'Four times Three is Equal to Twelve'. But what exactly does that mean? And how do we do it?

Multiplication is simply the number of times you add something of the same amount together. It is adding to itself a given number of times.

Let's say you have four boxes. Each box has 3 apples. How many boxes are there? There are 4 boxes. How many apples are in each of the boxes? There are 3 apples in each box. But how many apples are in all the boxes together? Let's see:

Box 1: 1 apple 1 apple 1 apple

Box 2: 1 apple 1 apple 1 apple

Box 3: 1 apple 1 apple 1 apple

Box 4: 1 apple 1 apple 1 apple

Box 1 = 3 apples

Box 2 = 3 apples

Box 3 = 3 apples

Box 4 = 3 apples

3 + 3 + 3 + 3 = 12 apples

How many times did we add 3? We added it 4 times because there are four boxes:

3 x 4 = 12

This means, "Three added to itself four times is equal to the total 12"

What if we add another box? Then we would have to add 3 to itself five times.

3 + 3 + 3 + 3 + 3 = 15 apples

This is the same as 3 x 5 = 15

It means, "3 added to itself 5 times is equal to the total of 15"

What if there were 7 boxes all containing 3 apples?

That would be 3 apples added to itself 7 times (boxes).

Which is: 3 x 7 = 21 total apples

If you add 1 to itself 12 times, how much will you get?

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12

1 x 12 = 12

If you add 5 to itself 6 times, how much will you get?

5 + 5 + 5 + 5 + 5 + 5 = 30

5 x 6 = 30

Did you also know that if you change them around they still equal the same thing? For example:

5 x 6 = 30

6 x 5 = 30

3 x 4 = 12

4 x 3 = 12

1 x 9 = 9

9 x 1 = 9

This means that if you add one to itself 9 times it will equal 9. And if you add 9 to itself 1 time, it will also equal 9, but if you add 9 to itself 2 times, it will equal 18.

What about with the number 0? If you add 0 to itself a given number of times, how much will it be? Well lets, see.

0 + 0 = ?

0 + 0 + 0 = ?

0 + 0 + 0 + 0 = ?

0 x 2 = 0

0 x 3 = 0

0 x 4 = 0

You see, zero times a number will always be equal to zero! 0 + 0 = 0 x 2, which equals zero. Even 0 = 0 x 1, which also equals zero.

2 is already added to itself 1 time. 2 x 1 = 2. but 2 x 2 = 4 But what if two was added to itself 0 times? It wouldn't be two: it would be zero! 2 x 0 = 0

7 is already added to itself 1 time. 7 x 1 = 7, but 7 x 2 = 14 But what if seven was added to itself 0 times? It wouldn't be seven: it would be zero! 7 x 0 = 0

2 x 0 = 0

0 x 2 = 0

7 x 0 = 0

0 x 7 = 0

There you have it! That's how multiplication works! Multiplication is simply adding a given number to itself a given number of times. If there are 7 houses each on 5 blocks, then to get the total number of houses you can multiply 7 x 5 = 35 houses. If there are 7 planets in each of 12 star systems, then to get the total number of planets of them all together would be 7 x 12 = 84 planets. If there are 20 people, and each have 3 dollars in their pocket, then you can get the total amount of money of them all together by 20 x 3 which would be 60 total dollars, or 3 x 20 which would also be 60 dollars. In any case, the result of a multiplication will be the product.

The Basics of Division

What is division?

Division means to separate things into groups. It is the number of times you divide something, or a group of things, into smaller equal groups.

If you have 24 candles and you divide them into 3 groups, then in each group there will be 8 candles:

24/3 = 8

If you were to divide the candles into 8 groups, then there will be 3 candles in each group:

24/8 = 3

If you were to divide a pizza into 24 parts, then you will have:

1/24 Which will be a fraction less than one because we are actually dividing 1 into 24 smaller parts. Each piece will be rougly .0417. Basically .0417 x 24 = 1 (roughly)

But let's divide large numbers into groups so that the amounts are number 1 or greater.

Let's divide 100 into 20 groups/parts.

100/20 = 5

This means that 5 times 20 is equal to 100.

What if we divide 100 into 5 groups?

100/5 = 20

This means 20 x 5 is equal to 100

How about dividing 100 into 100 parts/groups?

100/100 = 1

This means 1 x 100 = 100

There are one hundred 1's in 100.

What if we divide 100 into 1 part? It is already one part:

100/1 = 100

This means there is 1 one hundred in 100.

What if we divide 100 into parts of zero? How many zero's do we get? 0 + 0...how many times is equal to 100? It is currently undefined:

This means there is 'an undefined number' of zeros in 100. We know it is not any normal number because 0 x any finite number is always equal to zero. So how many zero's can be in 100? Infinity? Use your imagination.

100/0 = undefined

What if we divide 0 itself into 100 parts? This means 0 + itself 100 times is equal to: ?

0/100 = 0

Well, there you have it! That's how division works! Division is just simply dividing something into groups a given number of times. The thing being divided is the dividend. The number of groups/parts it's being divided into is the divisor number. How much is in each group is the quotient, or the result of the dividend being divided by the divisor.