Question

Note: This is a TUTORIAL, NOT a question.
What are proportions? How do I solve for variables?

Added note: You need to know the concept of fractions, ratios and one variable equations before continuing further.

Answer 1

So, what are proportions?
The easiest way to talk about proportions are that they are equivalent fractions!

You write a proportion like this:-
\(x:y::a:b\)

x:y means x over y, if you know the concept of ratios. Similarly, a:b is a over b.


Okay, now let's say that @lgbasallote asks you if 2:8 and 4:16 are in proportion, you'll just check if \(2 \over 8\) and \(4 \over 16\) are equivalent.

The answer turns out to be YES! They are equivalent!


Let me tell you another interesting fact.
In the proportion - a:b::x:y, x and y are extremes and x and b are means.

Why am I telling this to you?
VERY IMPORTANT FACT: PRODUCT OF MEANS = PRODUCT OF EXTREMES.

Here, ay = bx.

But why?

If you recall the concept of equations and fractions, then you can conclude that when we cross-multiply, we can solve the equation.

\(\Large \color{MidnightBlue}{\rightarrow {a \over b} = {x \over y} \rightarrow ay = bx }\)

But ratios are same as fractions, right?
I hope you get it by now.

Now, let's start with solving for variables!

If @FoolForMath asks you - "What is the value of x in 5:x::25:625?"

You can answer it by solving for x(I don't say?)

Product of means = Product of extremes.

\(\Large \color{MidnightBlue}{\rightarrow 25x = 3125 }\)
\(\Large \color{MidnightBlue}{\rightarrow x = 3125 \div 25 = 125 }\)

Wasn't that easy? Please post further questions/comments, they will be appreciated.

Answer 2

@ ParthKohli: you have explained well, i think. good job. thanks. it will help others.

Answer 3

yes, very thorough and clear, as usual :)
@LovelyMegan I think that this tutorial would help you with your question^

Answer 4

Thank you @Toriqur @TuringTest I tried my best this time. My tutorials earlier had something or the other thing wrong. I hope this one isn't *fingers crossed*

Answer 5

no typos I can find

Answer 6

There was one but I noticed it and corrected.

Answer 7

lol nice touch in adding a bit of reality..."when lgbasallote asks you" and "when FoolForMath asks you"

Answer 8

Wow, that was a really good explanation! It was very clear and easy to read and understand:)
Thumbs up: d(^_^)b

Answer 9

thanks lol

Answer 10

UR right

Answer 11

i am not used to the double colon notation where does that come from?
\[x:y::a:b\]

Answer 12

Double-colon actually means '='

Answer 13

Or, 'is proportionate to'

Answer 14

ok gotcha

Answer 15

Just like a cupcake::sweet :D