Multiplying decimals by integers

Whether we are calculating an addition, subtraction, multiplication or a division, we should recognise the importance of:

• a more formal written method (sometimes called standard written algorithms!)
• an efficient mental method

A mental method doesn’t mean that we are expected just to write down the answer!

Many of the best mental methods come with ‘jottings’ to help us remember the ‘part answers’ we need as we work towards the final answer!

Get plenty of regular and varied practice with (standard) formal written methods to build your confidence, but remember that there are also times when a mental method may be better.

Mental methods usually help to build a real understanding of the size and position of a number in our amazing number system!

8.7 lies between 8 and 9.

8.7 rounded to the nearest integer is 9.

Therefore we could estimate that the answer would be between 48 (8 x 6) and 54 (9 x 6)

A is an example of a mental method and B an example of a formal written method.

0.7 x 6 is just six lots of seven tenths or 42 tenths or 4.2.

If we know that the answer to 8.7 multiplied by 6 is 52.2, then there are many other calculations that would be easy to figure out!

Here are some examples of calculations that are related to the fact that 8.7 x 6 = 52.2:

• 8.7 x 12 = 104.2 (52.2 x 2)

• 8.7 x 60 = 522 (52.2 x 10)

• 0.87 x 6 = 5.22 (52.2 ÷ 10)

• 8.7 x 26 = 1792.2 (8.7 x 20) + (8.7 x 6) = (87 x 10 x 2) + (8.7 x 6) = 1740 + 52.2

5.48 lies between 5 and 6.

5.48 rounded to the nearest integer is 5 and 5.5 if rounded to one decimal place.

Therefore we could estimate that the answer would be between 45 (5 x 9) and 54 (6 x 9).

So…

• 5.48 x 900 = 4932 (49.32 x 100)

• 0.548 x 9 = 4.932 (49.32 ÷ 10)

• 5.48 x 18 = 98.64 (49.32 x 2)

• 5.48 x 19 = 104.12 (5.48 x 10) + (5.48 x 9) = 54.8 + 49.32