Chapter Contents

Ratio and Proportion

Chapter Contents

Introduction
What is rational number?
How to represent rational number on number line.
FAQs
Solved Examples
MCQs

Chapter
Contents

Introduction

To start with what are rational numbers and how do we write them, there is a brief introduction about them in the chapter Types of Number with Examples.
We will discuss more about them here and learn if we can represent them on the number line and how.

What is rational number?

A number which can be written in the form of $\frac{p}{q}$ , where p and q are integers and q ≠ 0.

Example

$\frac{1}{2}$ , $\frac{6}{7}$ , $\frac{9}{10}$ , $\frac{3}{10}$ etc.

Note

Even 0 is also a rational number as 0 can be written as $0 = \frac{0}{1}$

How to represent rational number on number line.

Rational numbers can be written on the same number line as usual numbers.
The following steps will help in representing a rational number on the number line.

Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Divide distance between 0 and 1 into n equal points.
Mark the points as $\frac{1}{n}$ , $\frac{2}{n}$ , $\frac{3}{n}$ , $4/mn>n$ etc.

Let’s learn the above steps with an example.

Example

Example 1: Represent $\frac{3}{7}$ on number line.
Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Here, n = 7.
So, divide distance between 0 and 1 into 7 equal points.
Length of each part between two adjacent points is $\frac{1}{7}$ .
Now, start from 0 and mark the point $\frac{3}{7}$ on the number line.
So, OA = $\frac{3}{7}$

Example 2: Represent $\frac{7}{4}$ on number line when value of denominator is less than value of numerator.
Step 1
Draw a number line with positive numbers on the right hand side and negative number on the left hand side of 0.
Step 2
Here, n = 4.
So, divide distance between 0 and 1 into 4 equal points and do the same from 1 to 2, i.e. divide them into 4 equal parts.
Length of each part between two adjacent points is $\frac{1}{4}$ .
Mark the point $\frac{7}{4}$ on the number line.
So, OA represents $\frac{7}{4}$

Frequently Asked Questions

Q) What is ratio?

When two quantities of same kind and same unit of measurement are divided then the value we get is called ratio. Ratio is represented by symbol :. Ratio of two quantities a and b is written as a:b and read as a ratio b, where a and b are called as terms.

Q) What is antecedent in ratio?

Antecedent is the first term of a ratio. For example a is the antecedent in ratio a:b.

Q) What is consequent in ratio?

Consequent is the second term of a ratio. For example b is the consequent in ratio a:b.

Q) What is proportion?

Proportion means that the ratios are equal. Proportion is represented by symbol ::. If two ratio a:b and c:d are equal, i.e. a ÷ b = c ÷ d then we can say a,b,c and d are in proportion.