We subtract 217 from 241 for our remainder.
241 − 217 = 24
So 241 divided by 31 is 7 with 24 remainder.
We could have seen this by observing that 8 times 30 is 240 and 241 is only 1 more. So we can
anticipate that 8 times 31 will be too high.
How about dividing 239 by 29?
We round off to 30 and divide by 10 and by 3 for our estimate.
Two hundred and thirty-nine divided by 10 is 23.
Twenty-three divided by 3 is 7.
But like the previous case, we can see the real answer is probably different.
Twenty-nine is less than 30 and 30 divides into 239 almost 8 times, as it is only 1 less than 240,
which is exactly 8 times 30. So we multiply 8 times 29 to get 232, which is a valid answer.
Had we not seen this and chosen 7 as our answer, our remainder would have been too large.
Seven times 29 is 203. Subtract 203 to find the remainder.
239 − 203 = 36
This is higher than our divisor so we know we have to raise the last digit of our answer.
What if we are dividing by 252? What do we round it off to? Two hundred is too low and 300 is too
high. The easy way would be to double both the number we are dividing and the divisor, which won’t
change the answer but will give us an easier calculation.
Let’s try it.
2,233 ÷ 252 =
Doubling both numbers we get 4,466 ÷ 504. We now divide by 500 (5 × 100) for our estimates and
correct as we go.
We divide 4,466 by 500 for our estimate. We divide using factors of 100 × 5:
4,466 ÷ 100 gives 44
44 ÷ 5 gives 8 (8 × 5 = 40)
Now, 8 × 504 = 4,032, subtracted from 4,466 gives a remainder of 434. If the remainder is important
(we are not calculating the answer as a decimal), because we doubled the numbers we are working with,
the remainder will be double the true remainder. That is because our remainder is a fraction of 504 and
not 252. So, for a final step to find the remainder, we divide 434 by 2 to get an answer of 8 r217. If you
are calculating the answer to any number of decimal places then no such change is necessary. That is
because 217/252 is the same as 434/504.
Test yourself
Try these problems for yourself. Calculate the remainder for a) and the answer to one decimal place for b).
a) 2,456 ÷ 389 =
b) 3,456 ÷ 151 =
The answers are:
a) 6 r122
b) 22.9
The answer to b) is 22.8874 to four decimal places, 22.887 to three decimal places, 22.89 to two