(KS2, Year 4)

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:multiplying_applesIn numbers:3_times_4_equals_12Multiplication 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:multiplication_as_repeated_additionAnother 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: 32_times_23 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). 32_tens_units This allows the numbers to be broken down: 32_and_23_tu_parts Multiplication then takes place as follows:32_times_23_tu_breakdownAdding the numbers:32_times_23_tu_breakdown_sumThe 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.

  • 32 times 23 tu long multiplication 1
  • 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.
    32 times 23 tu long multiplication 2
  • 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):

  • 32 times 23 tu long multiplication 3
  • 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.)
    32 times 23 tu long multiplication 4
  • Use long addition to add the two numbers between the lines:

  • 32 times 23 tu long multiplication 5
The solution to 32 × 23 is 736.

Lesson Slides

This slider below shows another example of multiplication:
long multiplication

Parts of Multiplication

product explained
  • 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: 2_times_3_equals_6_mini If the 2 and 3 are swapped around, the product is the same: 3_times_2_equals_6_mini This is the commutative property of multiplication - changing the order does not change the result.


When multiplying numbers in a column, sometimes the product may be 10 or more: long_multiplication_carry_1 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:
    long multiplication carry 2

  • Write the 1 in 12 underneath the column to the left (this is carrying the 1):
    long multiplication carry 3

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

    long multiplication carry 4
author logo

This page was written by Stephen Clarke.

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.

next up:

basic division