Test yourself
Try these problems for yourself:
a) 76 ÷ 9 =
b) 76 ÷ 8 =
c) 71 ÷ 8 =
d) 62 ÷ 8 =
e) 45 ÷ 7 =
f) 57 ÷ 9 =
The answers are:
a) 8 r4
b) 9 r4
c) 8 r7
d) 7 r6
e) 6 r3
f) 6 r3
This method is useful if you are still learning your multiplication tables and have difficulty with
division, or if you are not certain and just want to check your answer. As you get to know your tables
better you will find standard short division to be easy. Next time you watch a sporting event, use these
methods to see how your team is going.
Remainders
Let’s go back to our problem at the beginning of the chapter. How would we divide 33 maths books
among 4 students? You couldn’t really say that each student is given 8.25 or 8¼ books each, unless you
want to destroy one of the books! Each student receives 8 books and there is 1 book left over. You can
then decide what to do with the extra book. We would write the answer as 8 r1, not 8.25 or 8¼.
If we were dividing up money, we could write the answer as 8.25, because this is 8 dollars and 25
cents.
Some problems in division require a whole remainder to make sense, others need the remainder
expressed as a decimal.
Bonus: Shortcut for division by 9
There is an easy shortcut for division by 9. When you divide a two-digit number by 9, the first digit of
the number is the answer and adding the digits gives you the remainder. For instance, dividing 42 by 9,
the first digit, 4, is the answer and the sum of the digits, 4 + 2, is the remainder.
42 ÷ 9 = 4 r6
61 ÷ 9 = 6 r7
23 ÷ 9 = 2 r5
These are easy.
What do we do if the sum of the digits is 9 or higher? For instance, if we divide 65 by 9, the first
digit, 6, is our answer and the remainder is the sum of the digits, 6 + 5 = 11. Our answer is 6 r11. But
that doesn’t make sense because you can’t have a remainder larger than your divisor. Nine divides into
11 one more time, so we add 1 to the answer (6 + 1), and the 2 left over from 11 becomes the new
remainder. So the answer becomes 7 r2.
We could also have applied our shortcut to the 11 remainder. The first digit is 1, which we add to our
answer, and the sum (1 + 1) gives a remainder of 2.