Five is 10 divided by 2. To multiply by 5, we can

- multiply first by 10 then divide the product by 2 or
- divide the multiplicand by 2 first and then add a zero at the end of the quotient.

This shortcut requires only the skill of dividing by 2.

Except when half of the multiplicand is readily computed, we recommend that the first procedure be followed because adjusting the decimal point first gives the magnitude of the product, i. e., hundreds or thousands.

As discussed in Short cut # 6, dividing by **2 **means getting** half of the number**

**Half of 10 **is** 5.**

**Half of 20 **is** 10.**

**Half of 50 **is** 25.**

**Half of 64 **is** half of 60 **plus **half of 4 **or **34.**

**Half of 72 **is** half of 60 **plus **half of 12 **or **36.**

**Half of 96 **is** half of 80 **plus **half of 16 **or **48.**

**Half of 7 **is**half of 6** plus **half of 1** or **3.5**

Example 10.1: **36 x 5** =

Half of **36**is**half of20** plus **half of16** which is **18. **This becomes **180** when a zero is affixed at the end.

Example 10.2: **245 x 5** =

When a zero is affixed at the end, the number becomes **2,450**. We can recite the answer as we mentally compute

a) half of 2 thousand is **“1 thousand”,**

b) half of 4 hundred is ** “2 hundred” **

c) And half of 50 is “**25”**.

Example 10.3: **455 x 5 =**

**455** became **4,550** after multiplying by ten. We can think of it as** 4000 + 400 + 150**

a) Half of 4000 is **“Two Thousand”**

b) Half of 400 is **“two Hundred”**

c) Half of 150 is “**seventy-five**”

Example 10.4: **3,758 x 5** =

Here all digits are odd except the last digit.

After adding a zero at the end, the number becomes **37 thousand, 5 hundred and 80**. We can think of it as **36,000 + 1,400 + 180** as in the previous example to get a quick **18,000 + 700 + 90 **answer. Here we will try to divide it by 2 using the one-line method used in MSC 6.

**3 _{1}7_{1}5_{1}80 ÷ 2 = 18, 790**

a) ** 3 **divided **2** is **1 **with a remainder of **1** which will become the first digit of the next dividend.

b) **7 **becomes** 17 **which when divided by **2** will give **8** with a remainder of **1**. We can now start to say our answer aloud as **“ eighteen thousand,”**

c) **5** now becomes **15 **and when divided by **2** gives **7, **remainder** 1, **so we continue as “**seven hundred and”**

d) The last two digits of the dividend then becomes**180 ** which when divided by 2 is **“ninety”.**

Example10.5: **462 x 50 =**

Fifty is half of 100 so we

a) Add two zeroes at the end of **462** so it will become **46,200**.

b) Half of that is **Twenty three thousand one hundred.**

Example 10.6: **5% 0f 864**=

5% is half of 10% so we

a) move the decimal point one place to the right so that it will become **86.4**

b) divide it by 2 to get **43.2**

Exercise 10: compute for the following products:

- ) 864 x 5 =
- ) 748 x 5 =
- ) 356 x 5 =
- ) 475 x 5 =
- ) 2,357 x 5 =
- ) 685 x 50 =
- ) 873 x 50 =
- ) 347 x 500 =
- ) 5% of 739 =
- ) 5% of 95.5 =