Introduction to Rational Numbers

Introduction to Rational Numbers

Rational numbers constitute a basic foundation in a child’s mathematical learning.
Understanding the core topic of rational numbers is vital for learning various advanced
concepts and connecting topics. It also depicts the math success of a child. A child
usually gets introduced to rational numbers at the elementary stage that develops a
foundational understanding of numbers. It is the time when students require to use their
former knowledge of numbers to build new concepts that diverge from their prior

Most of the students find it challenging and often get disheartened by the fact that they
no longer relate to this change. The lack of basic understanding of rational numbers is a
great cause for concern as these concepts are applied in various topics of advanced
mathematics and hold great academic importance. It is almost impossible for a student
to succeed in algebra without understanding rational numbers.

The use of rational numbers also prevails in our daily lives. We require them to
understand our daily calculations like following a recipe, checking shopping discounts,
exchange money, assessing the most cost-effective size of products, preparing
budgets, investing our savings, reading financial statements, etc. Hence we need to be
able to conceptualize the use of rational numbers in our daily lives.

What are Rational Numbers?

A rational number in arithmetic is a number that is expressed as the ratio of two
integers, where the denominator can never be a zero. The word ‘rational’ derived from
word ratio means comparing two or more values, also known as fractions. In simple
terms, it is the ratio of two integers.

The non-rational numbers are called irrational numbers. Irrational numbers are written in
decimals forms and not in a fractional form that means irrational numbers cannot be
written as the ratio of two integers. Irrational numbers have countless digits after the
decimal point. Such decimals are called non-terminating decimals. Rational numbers
are terminating, whereas irrational numbers are non-terminating.

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For example, ? is a rational number, and 1/0 is an irrational number since the
denominator is zero. Another example of irrational numbers is 0.21111121…since it is

Applications of Rational Numbers:

Learning about rational numbers is necessitated due to their various applications in
many quantities or measurements, which natural numbers or integers alone can not
represent. For example, the measurement of quantities like weight, length, mass, or
time. Rational numbers possess the ease and flexibility of representing various
quantities because they have two-part numbers, with one part available for designating
the size of the increments and the other for counting them. When a rational number is
written as a fraction, these two parts are clearly visible and are called denominators and
numerators, which specify their roles. In rational numbers such as 8 or 1.05, the second
part is missing or obscure, but it is readily supplied or brought to light.

As an integer, 8 needs no second part; as a rational number, it does, and the second
part is supplied by the obvious relationship 8 8/1. In the case of 1.05, it is the decimal
point that designates the second part, in this case, 100. The only information that
decimal point has to offer is its position; the numbers it can designate are limited to
powers of 10: 1, 10, 100, etc. For that reason, there are many rational numbers that
decimal fractions cannot represent, ?, for example.


Clearly, the core concepts of rational numbers, their representations, and operations are
complicated. Students need to acquire this initial grounding in the rational-number
system through constant practice. An in-depth understanding of rational numbers
requires thorough practice and learning of various advanced concepts. Cuemath offers
interactive worksheets for kids to learn rational numbers in a fun and engaging way.
You can easily find some 5th and 6th-grade math worksheets on the Cuemath website.