What is a rational number?

Whether you’re a student or are looking to improve your numeracy skills, understanding rational numbers is crucial. Let’s discover what makes rational numbers so fascinating!

icon of a star with a smiley face

Author
Kara

Published
December 5, 2023

What is a rational number?

Whether you’re a student or are looking to improve your skills, understanding rational numbers is crucial. Let’s discover what makes rational numbers so fascinating!

icon of a star with a smiley face

Author
Kara

Published
Dec 5, 2023

What is a rational number?

Whether you’re a student or are looking to improve your numeracy skills, understanding rational numbers is crucial. Let’s discover what makes rational numbers so fascinating!

icon of a star with a smiley face

Author
Kara

Published
Dec 5, 2023

Key takeaways

  • A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.
  • There are two main types of rational numbers: proper and improper fractions. 
  • There are also mixed numbers, which are a combination of a whole number and a proper fraction.

Are you ready to unlock the secrets of the number universe? Let’s dive deep into the world of rational numbers, where fractions and decimals unite to create a mathematical wonderland.

Rational numbers may seem daunting at first, but don’t let their complexity fool you – they’re the building blocks of many important mathematical concepts.

Whether you’re a student, a maths enthusiast or are simply looking to improve your numeracy skills, understanding rational numbers is crucial.

So, let’s embark on this mathematical adventure together and discover what makes rational numbers so fascinating!

Rational numbers definition

Have you ever asked yourself, ‘What is a rational number?’. If the answer is yes, you’re in luck!

A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero.

In other words, it’s a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero. Rational numbers can also be expressed as terminating or repeating decimals.

Types of rational numbers

Rational numbers are numbers that can be expressed as a ratio of two integers. There are two main types of rational numbers: proper and improper fractions. 

In addition to proper and improper fractions, there are also mixed numbers, which are a combination of a whole number and a proper fraction.

Examples of numbers that are rational

A proper fraction is a rational number where the numerator is less than the denominator. Some examples of proper fractions include:

1/2 

3/4

7/8

2/3

An improper fraction, on the other hand, is a rational number where the numerator is greater than or equal to the denominator. 

Some examples of an improper fraction include:

5/2

3/2

7/4

2/1

Mixed numbers are a combination of a whole number and a proper fraction. 

Some examples of mixed numbers include:

1 1/2

2 2/3

1 1/4

3 2/5

Explore rational numbers with DoodleMaths

MeetDoodleMaths, the award-wining maths app that’s proven to double a child’s rate of progression with just 10 minutes of use a day!

Filled with fun, interactive questions covering the whole curriculum, it creates each child a unique work programme tailored to their needs, boosting their confidence and skills in the subject. Try it for free today!

for families

Adding and subtracting rational numbers

Adding and subtracting rational numbers is a fundamental skill in mathematics that can be easily mastered with a little practice. To add or subtract rational numbers, we need to follow a series of steps.

Step 1: Make sure that the fractions have the same denominator. To do this, we can find a common multiple of the denominators and convert each fraction into an equivalent fraction with that common denominator.

Step 2: Add or subtract the numerators and keep the common denominator.

To add:

rational number example

To subtract:

Multiplying and dividing rational numbers

Step 1: Multiply the numerators together.

what are rational numbers example

Step 2: multiply the denominators together.

Step 3: simplify the fraction as needed. In this example, doing so gives us 1/2!

To divide

Step 1: Find the reciprocal of the second fraction by ‘flipping it’.

how to divide rational numbers

Step 2: multiply the numerators together.

Step 3: Multiply the denominators together.

Step 4: Simplify the fraction as needed. In this example, we can’t simplify the fraction. This gives us a final fraction of 8/9 (or 8 over 9)!

FAQs about rational numbers

Yes, zero is a rational number. A rational number is any number that can be expressed as a ratio of two integers, and zero can be expressed as the ratio of 0 to any non-zero integer, such as 0/1, 0/2, 0/3, and so on.

Yes, fractions are rational numbers. A rational number is any number that can be expressed as the ratio of two integers, and a fraction is a type of number that is expressed as the ratio of two integers, where the denominator is not equal to zero. For example, 1/2, 5/8, and -3/4 are all examples of fractions that are also rational numbers.

Not all decimals are rational numbers, but some are.

A decimal is a number expressed in base 10, with a decimal point and digits that follow.

A decimal is rational if and only if it terminates (ends) or repeats a pattern. For example, the decimal 0.5 terminates, so it is a rational number that can be expressed as the fraction 1/2.

Likewise, the decimal 0.333… repeats the pattern “3” infinitely, so it is a rational number that can be expressed as the fraction 1/3.

However, the decimal 0.12345678910111213141516… goes on infinitely without repeating a pattern, and is therefore not a rational number.

Yes, rational numbers can be negative. A rational number is any number that can be expressed as the ratio of two integers, and this includes both positive and negative numbers. For example, 1/2, -3/4, and 5/6 are all examples of rational numbers, whereas -3/4 and 5/6 are negative rational numbers.

Yes, all integers are rational numbers. A rational number is any number that can be expressed as the ratio of two integers, and every integer can be expressed as the ratio of that integer and 1.

The main difference between rational and irrational numbers is that rational numbers can be expressed as a fraction, while irrational numbers cannot be expressed in this way.

Group 208

Try DoodleMaths for free!

Related posts

Rational vs irrational numbers

Explore the differences between rational and irrational numbers

What is standard form?

Discover how standard form helps us represent numbers and equations clearly

What is place value?

Learn all about place value and take a look at some examples!

Login

Are you a parent, teacher or student?

Get started for free!

Are you a parent or teacher?

Maths information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience

Exam prep information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience

Case studies information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience

Information pack

We ask for your contact info so that our Education Consultants can get in touch with you and let you know a bit more about Doodle.

Student Login

Which programme would you like to use?

If you’d like to use Doodle’s browser version, please visit this page on a desktop.

To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here: