We can easily divide a number by 4 by halving the number twice and by 8, by halving thrice. We shall, however try dividing by 4 and 8 using the one line solution introduced in MSC 6 – Division by Two.
Example 12.1: 586 ÷ 4 =
When dividing a whole number by 4, there are only 4 possible remainders: 0, which means that the number is evenly divisible by 4; and 1, 2 and 3 which are equivalent to 0.25, 0.50 and 0.75 respectively. In this example, the dividend is an even number so the remainder can only be 0 or 2.
1 1 4 1 4 6
4) 5 18 6 4) 5 18 26 4) 5 18 26 ( r 2
a) Dividing 5 by 4 gives a quotient of 1 and a remainder of 1 which we place in front of the next digit of the dividend,
b) Dividing the next dividend 18 by 4 results in a quotient of 4 and a remainder of 2, which we then place in front of the next digit
c) Finally, we divide 26 by 4 to give 6 and a remainder of Thus the final quotient is 146 2/4 or 146.5.
Example 12.2: 743 ÷ 4 =
1 8 5
4) 7 34 23 (r 3
Here the dividend is an odd number, so we expect a remainder of 1 or 3.
- Dividing 7 by 4 gives 1 remainder
- 34 divided by 4 gives 8 remainder23 divided by 4 gives 5 remainder
- The quotient is 185 3/4 or 185.75.
The following are the values of the remainders when dividing by 8.
Remainder decimal equivalent
1 0.125
2 0.25
3 0.375
4 0.5
5 0.625
6 0.75
7 0.875
Example 12.3: 983÷ 8 =
1 2 2
8) 9 18 23 (7
Using the one line solution, we have
- 9 divided by 8 is 1 remainder 1
- 18 divided 8 is 2 remainder 2
- 23 divided by 2 is 2 remainder 7
So we arrive at an answer of 122 remainder 7. This is equivalent to 122 7/8 or 122.875
Example 12.4: 6352 ÷ 8 =
7 9 4
8) 63 75 32 (0
Using the one line method, we got the quotient 794. For the careful observer, the dividend, 6,352 is very near 6,400 or exactly 48 less. 6,400÷ 8 = 800 and 48÷ 8 = 6 so 6352 ÷ 8 is simply 800 – 6 = 794.
Exercise 12:
- ) 456 ÷ 4 =
- ) 527 ÷ 4 =
- ) 983 ÷ 4 =
- ) 2,538 ÷ 4 =
- ) 6,789 ÷ 4 =
- ) 745 ÷ 8 =
- ) 1,278 ÷ 8 =
- ) 3,684 ÷ 8 =
- ) 6,454 ÷ 8 =
- ) 10,522 ÷ 8 =
Answers to all exercises are found in the answer key.
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