## The Lesson

Multiplication is repeated addition. For example, 3 × 4 is 3 added to itself 4 times (3 + 3 + 3 + 3). 3 × 4 = 12. 3 apples times 4 is 4 lots of 3 apples - 3 apples added to itself 4 times. It equals 12 apples:In numbers:Multiplication is denoted by the times sign, ×.## How to Multiply

The method used to multiply numbers will differ depending on the difficulty of the multiplication. Multiplying short numbers together is easier than multiplying long numbers together.## How to Multiply Short Numbers Together

It is relatively easy to multiply short numbers together. Children may learn multiplication as a process of repeated addition. For example:Another method is to use a number line. Multiplication then appears as scaling a number. If 2 is represented by an arrow from 0 to 2, multiplying by 3 is equivalent to scaling, or stretching, the arrow to being 3 times as long:Eventually, most people learn times tables which list all combination of multiplying short number together. Times tables should be committed to memory. Try a times tables test## How to Multiply Long Numbers Together

It is more difficult to multiply long numbers together. For example: This multiplication is made easier when we notice numbers are made of hundreds, tens and units (i.e. the place value of the digits in the number). This allows the numbers to be broken down: Multiplication then takes place as follows:Adding the numbers:The solution to 32 × 23 is 736.## Long Multiplication

Long multiplication involves writing each number in columns and multiplying a column at a time. As each column represents the tens and units of the numbers, long multiplication implicitly breaks the numbers down into tens and units, as above, but without you having to think about it.**Question**: What is 32 × 23?

- Write the numbers you wish to multiply, one underneath the other, the larger number above the smaller number.
- Select the right most digit of the bottom number (in the units column).

Multiply this with each digit of the top number in turn, starting on the right and moving left. Write the answer of each multiplication below the line, under the column of the top digit.

- Move one digit to the left on the bottom number (to the tens column).

Because we are multiply by a tens digit, the answer we get from multiplying by this digit will be tens times more. To show this, write a 0 in the answer row (below the previous answer): - Multiply the tens digit of the bottom number with each digit of the top number in turn, starting on the right and moving left. Write the answer of each multiplication below the line, to the left of the zero. (
**Note**: Each digit in the answer will be one column to the left of the digit of the top number that produced it.)

- Use long addition to add the two numbers between the lines:

## Parts of Multiplication

- The parts you multiply together are
**factors**. - The result of multiplying the numbers together is the
**product**.

## Order of Multiplication

The order in which numbers are multiplied does not matter. For example: If the 2 and 3 are swapped around, the product is the same: This is the*commutative*property of multiplication - changing the order does not change the result.

## Carrying

When multiplying numbers in a column, sometimes the product may be 10 or more: Multiplying the digits above gives 12. To do long multiplication correctly,- Write the 2 in 12 below, between the lines, in the same column as the top digit that was multiplied:

- Write the 1 in 12 underneath the column to the left (this is
*carrying*the 1):

- When multiplying the next pair of digits, be sure to add the 1 to the product: