What is a proportion?
By definition, a proportion is "a part, share, or number considered in comparative relation to a whole."
In math, however, we use proportions to represent proportional relationships. A proportional relationship shows equality between two part and whole ratios.
This proportion represents the proportional relationship between 2/5 and 4/10.
How to Make a Proportion
Making proportions may be vital to solving multiple math problems. To create a proportion, you first need two equal fractions or ratios, like so.
Then, turn them into fractions (if they weren't already fractions).
Finally, place a equal sign between the two fractions. You should not put a multiplication/division sign.
Dealing with Variables (Proportion's Best Friend)
Sometimes, you will see a problem that has a variable as one of the numerators or denominators, like this:
Here is a good example of a proportion with a variable.
While this may look intimidating, they are actually quite easy to solve. Anyone can solve proportions with variables using the power of...
Solve the problem like this.
First, cross multiply the two fractions.
If you have trouble remembering how to cross multiply, just remember a butterfly. Then, break apart the fraction, and turn it into an algebraic equation.
As you can see, we broke apart the fraction bars by turning the problem into multiplication.
Then, multiply your numbers.
x times 60 is 60x, and 8 times 15 is 120.
Now, we can solve this like a normal algebraic equation. To do this, you must get the variable by itself. In proportions, you will always be dividing to get the variable by itself.
To get the variable by itself, we can divide.
As well as that, remember to do the same to the other side. This means we are dividing by 60 on the left as well.
To solve this, we had to get the variable by itself by dividing by 60.
The two 60s on the left side get cancled out, which brings the x down.
Thus, we get our answer: x = 2. To check our work, we can plug x into the equation, and divide.
After checking, we see that our answer is correct.
To further your knowledge of this topic, let's do another practice. This time, we will put the variable, say, under the first fraction.
We will still do the same, as the variable does not change the way we solve the equation.
Turn the equation into an algebraic expression.
Get the variable by itself (using division).
And get your answer! Not so hard now, huh?