1,120 ÷ 35 =
Double both numbers. Twice 11 is 22, and two times 20 is 40; so 1,120 doubled is 2,240. Thirty-five
doubled is 70. The problem is now:
2,240 ÷ 70 =
To divide by 70, we divide by 10, then by 7. We are using factors.
2,240 ÷ 10 = 224
224 ÷ 7 = 32
This is an easy calculation. Seven divides into 22 three times (3 × 7 = 21) with 1 remainder, and
divides into 14 (1 carried) twice.
This is a useful shortcut for division by 15, 25, 35 and 45. You can also use it for 55. This method
also applies to division by 1.5, 2.5, 3.5, 4.5 and 5.5.
Let’s try another:
512 ÷ 35 =
Five hundred doubled is 1,000. Twelve doubled is 24. So, 512 doubled is 1,024. Thirty-five doubled
is 70.
The problem is now:
1,024 ÷ 70
Divide 1,024 by 10, then by 7.
1,024 ÷ 10 = 102.4
102.4 ÷ 7 =
Seven divides into 10 once; 1 is the first digit of the answer. Carry the 3 remainder to the 2, giving
32.
32 ÷ 7 = 4 r4
We now have an answer of 14 with a remainder. We carry the 4 to the next digit, 4, to get 44.
44 ÷ 7 = 6 r2
Our answer is
We have to be careful with the remainder. The 2 remainder we obtained is not the remainder for the
original problem. We will now look at obtaining a valid remainder when we divide using factors.
Finding a remainder
Sometimes when we divide, we would like a remainder instead of a decimal. How do we get a
remainder when we divide using factors? We actually have two remainders during the calculation.
The rule is:
Multiply the first divisor by the second remainder and then add the first remainder.
For example:
We begin by multiplying the corners 6 × 1 = 6
Then we add the first remainder, 1. The final remainder is 7, or 7/36.Test yourself
Try these for yourself, calculating the remainder: