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

1. multiply first by 10 then divide the product by 2 or
2. 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 ishalf of 6 plus half of 1 or 3.5

Example 10.1: 36 x 5 =

Half of 36ishalf 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.

3₁7₁5₁80 ÷ 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 becomes180  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:

1. )   864 x 5 =
2. )   748 x 5 =
3. )   356 x 5 =
4. )   475 x 5 =
5. )   2,357 x 5 =
6. )   685 x 50 =
7. )   873 x 50 =
8. )   347 x 500 =
9. )   5% of 739 =
10. )   5% of 95.5 =