Mental multiplication and division Multiplying. Multiplying by 10, 100 and 1000 are fundamental ideas in arithmetic. These ideas will eventually be used in work involving  negative numbers, positive numbers, decimals and percentages, so it is very important to master them early on. Never say 'to multiply by ten we add a nought'. This idea may work for whole numbers, but is totally false for decimals. eg.      3.98 x 10 is definitely not 3.980! If children are taught to add a nought there will be a great deal of un-learning needed later on. Bad habits are very difficult to break. The crucial ideas to get across are as follows: Multiplying. When multiplying by 10 the number moves one place to the left. When multiplying by 100 the number moves two places to the left. Dividing. When dividing by 10 the number moves one place to the right. When dividing by 100 the number moves two places to the right. Children should be able to understand the operation of division in its two aspects: a) Sharing.  If 45 sweets are shared between nine people, how many sweets does each person have? This is normally achieved with a philosophy of 'one for you, one for you....' b) Grouping.  If 45 sweets are available, how many people can have 5 sweets each? This is normally achieved by putting the sweets in piles of five and seeing how many piles there are. They should understand the following words and be able to read and write them: share, group, divide, divided by, divided into, divisible by, factor, quotient, remainder, inverse and they should know and recognise the division sign and its alternative (/). Definitions: Quotient is the answer to a division sum. eg.  the quotient of 20 and 4 is 5. Factors: The whole numbers that will divide exactly into a number. eg. the factors of 21 are  1, 3, 7 and 21 Notice that the number itself (21) is included in the factors. The factors not including the number itself are called proper factors. Inverse: Opposite. eg. the inverse of multiplication is division. eg. the inverse of addition is subtraction. More on mental multiplication and division