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.

1. Dividing 7 by 4 gives 1 remainder
2. 34 divided by 4 gives 8 remainder23 divided by 4 gives 5 remainder
3. 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

1. 9 divided by 8 is 1 remainder 1
2. 18 divided 8 is 2 remainder 2
3. 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:

1. )  456 ÷ 4 =
2. )  527 ÷ 4 =
3. )  983 ÷ 4 =
4. )  2,538 ÷ 4 =
5. )  6,789 ÷ 4 =
6. )  745 ÷ 8 =
7. )  1,278 ÷ 8 =
8. )  3,684 ÷ 8 =
9. )  6,454 ÷ 8 =
10. )  10,522 ÷ 8 =

 

Answers to all exercises are found in the answer key.

Discover the 25 Math Short Cuts ( 25 MSC )!