# Proportions

A ratio is one where you describe the relationship between 2 numbers. It is a statement that can be reduced or simplified.

And a proportion is nothing but 2 ratios that have values that is equal. Unlike a ratio, the proportion can be worked out and solved. And when you say that a proportion is 2 ratios that have values equal to other, let’s take this proportion:

5/10 is equal to 1/2

Hence, to solve a proportion, you need to have the knowledge of both ratios and proportion together. If we want to express 4 quantities (a,b,c,d) in a proportion then remember that a:b should be equal to c:d

a:b = c:d or a/b = c/d

When you write a proportion like this, a and d are called the extremes of the proportion whereas b and c are called as the middle terms of the proportion.

With Proportions, we can easily solve percent problems. Say for example, if the problem is to find out 25% of 180, we can write it like:

x / 180 = 25/100

Now we need to multiply the opposite corners, hence 25 x 80

X = 180 X 25 / 100
x = 4500/100
x = 45

Hence the answer here is 45.

This can also be achieved by another method where you can:

= 180 X 25 / 100
= 180 x (25/100)
= 180 * 0.25
= 45

1. Find the unknown value in the proportion: 2 : x = 4 : 8?

Let’s first convert the proportion into a fractional form,

2/x = 4/8

To solve the proportion, multiply the values across like:

2×8 = 4x

Or

4x = 2 x 8
4x = 16
x = 16/4

So x = 4

2. If a car is driving at a speed of 2 miles per hour, how far will it travel in 5 hours?

Set up the ratio:

2 miles / 1 hr = x miles / 5 hr

Cross multiply:

2 * (5) = (1) * x
10 miles = x

3. What is 25 percent of 50?

Since 50 is equal to 100%, we must figure out what is 25%. Set up the ratio as the following:

50 / x = 100 / 25

Cross multiply:

50 * 25 = 100 * x

Divide each side by 100
(50 * 25) /100 = 100/100 * x
x = 12.5