How do you work out 1579.5 divided by 27?

Answer 1

58.5

Answer 2

Usually by long division (in words):

write 27 outside a "bus stop" [shelter];

write 1579.5 under the bus stop;

put a decimal point over the bus stop over the decimal point of 1579.5;

27 doesn't go into 1;

27 doesn't go into 15;

27 into 157 goes 5 times;

put a 5 over the bus stop over the 7;

multiply 27 by 5 to get 135 and write it below the 157;

subtract 157 - 135 to get 22;

bring down the 9 to get 229;

27 into 229 goes 8 times;

put an 8 over the bust stop over the 9;

multiply 27 by 8 to get 216 and write it below the 229;

subtract 229 - 216 to get 13;

bring down the 5 to get 135;

27 into 135 goes 5 times;

put a 5 over the bus stop over the 5;

multiply 27 by 5 to get 135 and write it below the 135;

subtract 135 - 135 to get 0;

run out of digits in the bus stop and the result of the subtraction was zero, so the answer of 1579.5 ÷ 27 is 58.5

Written normally, this looks like:

.......... 58.5

.....---------

27 | 1579.5

...... 135

...... ----

........ 229

........ 216

........ ----

.......... 13 5

.......... 13 5

.......... -----

............... 0

[leading dots are used to line up the calculation; the decimal point is bold and slightly raised as in 58.5]

The decimal point is written in before any calculation is done so that it is not forgotten or its position is lost.

When working out the multiples of 27, round it to either 25 or 30 which should be easier to divide by. Once a multiple of these has been found, check with 27 itself.

With awkward numbers like 27, it can sometimes be easier to build up a "crib" sheet of multiples of 27 as you do the division:

1. write the numbers 1 to 10 in a column.
2. against 1 write 27
3. against 10 write 27 followed by a zero, that is 270 = 10 x 27
4. divide this by two (270 ÷ 2 = 135) and write this against 5 as 5 x 27 = 135.

Now when you have a division to do, you can check against those multiples of 27 you have found so far and if necessary add in extra ones, either by calculating the multiple of 27 (eg 8 x 27 = 216), or by adding 27 onto a known multiple, eg 7 x 27 = (6 x 27) + 27 = ((5 x 27) + 27) + 27, so 6 x 27 = 135 + 27 = 162 (write it in), and 7 x 27 = 162 + 27 = 189 (write it in).

You could fill in the "crib" sheet at the start, but you may not need all the values and could save time by filling in as you go.