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# Multiplication and Division

Multiplication and division are two important concepts relating to whole numbers. Let’s look at them now.

## Multiplication

Multiplication is the process of repeated addition. It is represented by the symbol ‘x’. And the following words also describe multiplication –  product, times, multiply, lots of, groups of, etc. 5 x 4 is really the number 4 added 5 times, i.e. 4 + 4 + 4 + 4 + 4 =  20.

For larger numbers, follow a process similar to addition and subtraction we saw earlier. Arrange the numbers one below the other in columns of units, tens, hundreds, and so on. Multiply the ones first, then the tens, and so on. For example 15×4 can be done as follows: Multiply the ones column first – 5 x 4 = 20. Put down 0, carry 2 up. Then multiply the tens – 1 x 4 = 4, and add the 2 that your carried up – 4 + 2 = 6. So the answer is 60.

 2 1 5 x 4 6 0

To multiply one or more numbers that end in zeros – multiply the non-zero digits of the 2 numbers, and write the number of zeroes from the numbers at the end of the value to get a final answer. If you have to multiply, 230 x 40, you would multiply 23 x 4, and add 2 zeroes at the end to get the final answer.

 1 2 3 x 4 9 2

Adding 2 zeroes to the end, will give us the final answer of 230 x 40 = 9200.

When you have to multiply two, three (or more) digit numbers, you have to do long multiplication, which involves a few steps:

• multiply the entire top number by the unit digit of the second (bottom) number, and write the value.
• in the next row, write a zero in the units place, and then multiply the top number with the tens digit of the bottom number, and write the value.
• now add the two values obtained above to get the final answer.

For example, the answer of 342 x 23 can be obtained as below:

 1 3 4 2 x 2 3 1 0 2 6 + 6 8 4 0 7 8 6 6

Let’s look at another example of multiplication of two numbers:

 1 0 6 x 2 4 4 2 4 + 2 1 2 0 2 5 4 4