ffirs.indd

Long Division by Factors 145
Double both numbers. Two times 11 is 22, and two times 20 is 40;
so 1,120 doubled is 2,240. Th irty-fi ve doubled is 70. Th e 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
Th is is an easy calculation. Seven divides into 22 three times (3 ×
7 = 21) with 1 remainder, and divides into 14 (1 carried) twice.
Th is is a useful shortcut for division by 15, 25, 35 and 45. You can
also use it for 55. Th is 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. Th irty-fi ve doubled is 70.
Th e 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 fi rst 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 14⁄.