Podcast
Questions and Answers
The numbers used for counting objects around you were called counting numbers or natural ______
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 ______
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 ______
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 ______
Fractions are numbers of the form numerator/denominator where the numerator is either 0 or a positive integer and the denominator, a positive ______
In this Chapter, we shall introduce the concept of rational ______ along with their addition, subtraction, multiplication and division operations
In this Chapter, we shall introduce the concept of rational ______ along with their addition, subtraction, multiplication and division operations
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 ______
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 ______
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.
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.
Any integer can be thought of as a __________ number.
Any integer can be thought of as a __________ number.
The word 'rational' arises from the term '__________'.
The word 'rational' arises from the term '__________'.
Each decimal number can be written as an ordinary fraction and, hence, are __________ numbers.
Each decimal number can be written as an ordinary fraction and, hence, are __________ numbers.
A profit of 150 was represented by 150 then a loss of 100 could be written as __________.
A profit of 150 was represented by 150 then a loss of 100 could be written as __________.
You know that a ratio like 3:2 can also be written as __________.
You know that a ratio like 3:2 can also be written as __________.
Rational numbers include __________ and fractions.
Rational numbers include __________ and fractions.
The ratio of two integers p and q (q ≠0), i.e., p:q can be written in the form __________.
The ratio of two integers p and q (q ≠0), i.e., p:q can be written in the form __________.
0.5 = __________
0.5 = __________
The distance of km below sea level can be denoted by __________.
The distance of km below sea level can be denoted by __________.
What is the purpose of introducing rational numbers in this Chapter?
What is the purpose of introducing rational numbers in this Chapter?
What are rational numbers defined as?
What are rational numbers defined as?
How did the number system get extended from whole numbers to integers?
How did the number system get extended from whole numbers to integers?
What do rational numbers include?
What do rational numbers include?
What motivated the introduction of integers in the number system?
What motivated the introduction of integers in the number system?
What was the initial purpose of natural numbers?
What was the initial purpose of natural numbers?
Which of the following best defines a rational number?
Which of the following best defines a rational number?
What is the result of multiplying -2/3 by 2?
What is the result of multiplying -2/3 by 2?
How can the distance of 750m below sea level be denoted in km?
How can the distance of 750m below sea level be denoted in km?
Are all fractions rational numbers? Why or why not?
Are all fractions rational numbers? Why or why not?
What is the equivalent rational number of -2/3 with a different numerator and denominator?
What is the equivalent rational number of -2/3 with a different numerator and denominator?
Can an integer be considered a rational number? Why or why not?
Can an integer be considered a rational number? Why or why not?
What is the result of adding -3/4 to -5/6?
What is the result of adding -3/4 to -5/6?
Can the decimal number 0.333 be expressed as a rational number?
Can the decimal number 0.333 be expressed as a rational number?
Why do rational numbers include both integers and fractions?
Why do rational numbers include both integers and fractions?
What does the term 'rational' arise from?
What does the term 'rational' arise from?
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.
