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How do you express #9/25# as a percent?

2 Answers
Jul 7, 2016

Answer:

Explained in detail. Once you have had some practice you can do these in just a few lines.

#36%#

Explanation:

There are 2 way to write percentage. The most common one is to have a number with % after it. So as an example, fifty percent would be #50%#. The other way is to write it is as a fraction. So for the example we would have #50/100#

The word percent can be split into to parts

Part 1: per #->" for each of"#

Part 2: cent#-> 100# (think of century ->100 years)

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("Using first principles")#

Convert #9/25# into percentage we need to change the bottom number (denominator) into 100.

So multiply #9/25# by 1 but in the form of #1=4/4#

#color(brown)(9/25xx1) color(blue)(" "->" "9/25xx4/4" "=" "36/100 )#

So as a percentage of a whole #color(magenta)(9/25 ->36%)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("Using the shortcut approach")#

Note that shortcuts are taken from first principles.

The shortcut is #9/25xx100%#

You have two options

Option 1: #" "9-:25xx100%#

Option 2: #" "(9 xx100-:25)%#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Explaining option 2

Write as:#" "9/25xx100/1#

#=(9xx100)/(25xx1) " "=" "(9xx100)/(1xx25)" "=" "9/1xx100/25#

They call this property as commutative

#=9 xx (cancel(100)^4)/(cancel(25)^1) = 9xx4=36#

Answer:

#9/25# as a percentage, would be #36%# and the full explanation is down below!

Explanation:

OK, so what actually a percentage means is the number in the percentage out of #100#.
Example: #5%# means #5/100#

Whenever, you have to convert a fraction to a percentage, make sure that your denominator is #100#. Let's move on to the the 2 procedures, shall we?

Procedure 1:
As I said, the denominator has to be #100#. So if we want the denominator of #9/25# to be #100#, then you have to multiply #25# by #4#.

Let me stop you before you move on. Whatever you add, subtract, multiply, or divide to the bottom has to be done to the top. And whatever you add, subtract, multiply, or divide to the top has to be done to the bottom! In this case, we are going to multiply 4 to the denominator.
So we have to multiply #4# to the numerator, too!

#9/25*4/4=36/100#

Now our denominator is 100, which means it is a %, so just take the numerator and put a #%# next to it, and you're done!

Procedure 2:
Just multiply the fraction to #100#!
#9/25xx100%=36%#

#100%= 100/100 = 1# so multiplying does not change the value.

(Of course, add the #%#, too!)

I hope you understood the procedures. I'm pretty sure there are other ways, but these to are the ones that I learned. You never know which one might help more in any problem. :)

Source: My knowledge. :)