Question

What are the differences between fractions and ratios?

Answer 1

Hint: The numbers are grouped as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and finally complex numbers. And, the fractions are a part of them, and ratios are a concept in which we use fractions. So, here we use the concepts based on these to solve this problem.

Complete step-by-step solution:
Fraction:
Generally, a fraction is defined as a part of a whole. It represents the equal parts of a whole.
A fraction has two parts namely numerator and denominator. The denominator represents the total number of parts into which a whole is divided into and the numerator represents the number of parts taken from the whole.
For example, consider that you have a piece of paper which is divided into 5 equal parts, out of which, two parts are given to your friend and three parts are left with you.
So, we say that, three out of five parts of paper are with you. And it is written in fraction as \[\dfrac{3}{5}\] .
In a fraction, if the numerator is less than the denominator, then the fraction is called a proper fraction and if the numerator is greater than the denominator, then the fraction is called an improper fraction.
An improper fraction is the sum of a few whole units and a fraction. For example, take \[\dfrac{9}{4}\] which is an improper fraction. So, \[\dfrac{9}{4}\] is equal to the sum of two whole units and \[{\dfrac{1}{4}^{th}}\] of a whole unit.
\[ \Rightarrow \dfrac{9}{4} = 2 + \dfrac{1}{4}\]
 Ratio:
It is defined as comparison between two or more quantities of the same units. It also tells us how much the first quantity is present in the second quantity.
It is represented as \[a:b\] which means \[a\] units are there for every \[b\] units. And it is read as .
Here, \[a\] is called antecedent and \[b\] is called consequent.
For example, if in a region, there are 200 math loving people for every 300 members, then the ratio is represented as \[200:300\] . Unlike a fraction, a ratio must be simplified to its least value.
So \[200:300\] can be written as \[2:3\] which means, out of every 3 members, 2 members love mathematics.

Note: A ratio can also be written in a fraction form, \[ \Rightarrow a:b = \dfrac{a}{b}\]
Remember that, a ratio will always be in a simplified way, whereas a fraction may or may not be in a simplified way. It depends on the context. A ratio can be between two or more than two quantities.
For example, if we take the ratio of people loving math, science, and English, it will be as \[a:b:c\] .