Mathematics Chapter 8: Rational Numbers 8.1 Introduction Quiz

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Questions and Answers

The numbers used for counting objects around you were called counting numbers or natural ______

numbers

By including 0 to natural numbers, we got the whole ______

numbers

The negatives of natural numbers were then put together with whole numbers to make up ______

integers

Fractions are numbers of the form numerator/denominator where the numerator is either 0 or a positive integer and the denominator, a positive ______

integer Signup and view all the answers

In this Chapter, we shall introduce the concept of rational ______ along with their addition, subtraction, multiplication and division operations

numbers Signup and view all the answers

For example, if the distance of 3 km to the right of a place was denoted by 3, then the distance of 5 km to the left of the same place could be denoted by ______

-5 Signup and view all the answers

A rational number is defined as a number that can be expressed in the form p/q, where p and q are __________ and q ≠ 0.

integers Signup and view all the answers

Any integer can be thought of as a __________ number.

rational Signup and view all the answers

The word 'rational' arises from the term '__________'.

ratio Signup and view all the answers

Each decimal number can be written as an ordinary fraction and, hence, are __________ numbers.

rational Signup and view all the answers

A profit of `150 was represented by 150 then a loss of` 100 could be written as __________.

-100 Signup and view all the answers

You know that a ratio like 3:2 can also be written as __________.

3/2 Signup and view all the answers

Rational numbers include __________ and fractions.

integers Signup and view all the answers

The ratio of two integers p and q (q ≠ 0), i.e., p:q can be written in the form __________.

p/q Signup and view all the answers

0.5 = __________

1/2 Signup and view all the answers

The distance of km below sea level can be denoted by __________.

-750m Signup and view all the answers

What is the purpose of introducing rational numbers in this Chapter?

To denote opposite situations involving numbers Signup and view all the answers

What are rational numbers defined as?

Numbers that can be expressed in the form p/q, where p and q are integers and q ≠ 0 Signup and view all the answers

How did the number system get extended from whole numbers to integers?

By putting together the negatives of natural numbers with whole numbers Signup and view all the answers

What do rational numbers include?

Fractions and negative numbers Signup and view all the answers

What motivated the introduction of integers in the number system?

The need to denote opposite situations involving numbers Signup and view all the answers

What was the initial purpose of natural numbers?

To count objects around you Signup and view all the answers

Which of the following best defines a rational number?

A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0 Signup and view all the answers

What is the result of multiplying -2/3 by 2?

-4 Signup and view all the answers

How can the distance of 750m below sea level be denoted in km?

-0.75 km Signup and view all the answers

Are all fractions rational numbers? Why or why not?

Yes, because all fractions can be expressed in the form p/q Signup and view all the answers

What is the equivalent rational number of -2/3 with a different numerator and denominator?

-4/6 Signup and view all the answers

Can an integer be considered a rational number? Why or why not?

Yes, because any integer can be written as a fraction with denominator 1 Signup and view all the answers

What is the result of adding -3/4 to -5/6?

-1 7/12 Signup and view all the answers

Can the decimal number 0.333 be expressed as a rational number?

Yes, because it has a repeating decimal representation Signup and view all the answers

Why do rational numbers include both integers and fractions?

Because integers can be represented as fractions with denominator 1 Signup and view all the answers

What does the term 'rational' arise from?

'Ratio' Signup and view all the answers

Study Notes

Number Systems

Counting numbers are also known as natural numbers.
Natural numbers along with 0 form whole numbers.
The combination of whole numbers and their negatives forms integers.

Rational Numbers

A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.
Any integer can be thought of as a rational number.
The term 'rational' arises from the term 'ratio'.
Rational numbers include integers and fractions.

Properties of Rational Numbers

A ratio like 3:2 can be written as 3/2.
Decimal numbers can be written as ordinary fractions, hence they are rational numbers.
A profit can be represented by a positive rational number, and a loss by a negative rational number.

Extensions of Number Systems

The initial use of natural numbers was for counting objects.
The inclusion of 0 in natural numbers led to the formation of whole numbers.
The addition of negatives to whole numbers formed integers.
The introduction of rational numbers extended the number system further.

Operations on Rational Numbers

Rational numbers can be added, subtracted, multiplied, and divided.

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Description

Test your understanding of the introduction to rational numbers in mathematics. This quiz covers the evolution of numbers from counting to natural numbers, whole numbers, integers, and the introduction of rational numbers.