1. ## percentage calculation wording

Hello Guys, I'm having an issue with percentage calculations, my problem is not with the numbers, it is with what the operation does.

Here it is:

if A was increased by 20%, to find the original value of A we divide by 1.2, that is A(original)= A/1.2 .

So the division is what confuse me, what does it do to get the original value of A. For example if I multiply 6 by 1/7, The result is how many sevens in a 6. Or if I divide 10 over 2 I get 5 (which indicates there are five 2's in a 10).

Sorry I know it is confusing but I need to understand the concept. I know the maths but I'm missing the wording of the operation.

I face these sort of questions frequently in Business related material.

2. ## Re: percentage calculation wording

if A was increased by 20%, to find the original value of A we divide by 1.2, that is A(original)= A/1.2
that is correct because 120% of $A_0$ is written, $1.20 \cdot A_0 = A \implies \dfrac{A}{1.20} = A_0$

For example if I multiply 6 by 1/7, The result is how many sevens in a 6.
No ... multiplying 6 by 1/7 is $\dfrac{6}{1} \cdot \dfrac{1}{7} = \dfrac{6}{7}$

note there are 42 sevenths in 6.

$6 \div \dfrac{1}{7} = 6 \times 7 = 42$

if I divide 10 over 2 I get 5 (which indicates there are five 2's in a 10).
if you divide 10 by 2 (divide 10 over 2 is incorrect phraseology), you get 5. 10 over 2 is the fraction where division of 10 by 2 is understood.

3. ## Re: percentage calculation wording

Still I didn't understand the meaning of A/1.2 ?? I know that it result [A][/o] .

4. ## Re: percentage calculation wording

Originally Posted by Thespark505
Still I didn't understand the meaning of A/1.2 ?? I know that it result [A][/o] .
this is about as simple as I can make it ...

(100% of original cost) + (20% of original cost) = new cost

changing the percents to their decimal equivalents ...

$(1.00)A_0 + (0.20)A_0 = A$

note the two terms on the left side have $A_0$ in common ...

$A_0(1.00 + 0.20) = A$

note that $(1.00+0.20) = 1.2$ represents a multiplier that takes into account the original cost and the 20% mark up

$A_0(1.2) = A$

the inverse operation of multiplication is division ... in other words, "undoing" the multiplier to get the original price requires division

$\dfrac{A_0(1.2)}{1.2} = \dfrac{A}{1.2}$

$\dfrac{A_0(\cancel{1.2})}{\cancel{1.2}} = \dfrac{A}{1.2}$

5. ## Re: percentage calculation wording

Wow... thanks for the effort. I know got the idea.

6. ## Re: percentage calculation wording

Division is reverse of multiplication:

5 * 4 = 20 : 20 / 4 = 5

100 * 1.2 = 120 : 120 / 1.2 = 100