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 _{1}8 6 4) 5 _{1}8 _{2}6 4) 5 _{1}8 _{2}6 ( 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 _{3}4 _{2}3 (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**remainder**23**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 _{1}8 _{2}3 (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 _{7}5 _{3}2 (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.

Discover the 25 Math Short Cuts ( 25 MSC )!

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