Hello Friends, in today's session we all are going to discuss about some of the most interesting topics of mathematics, rational numbers and numbers which are usually studied in VI grade of cbse board. Here I am going to tell you the best way of understanding these topics.
Now we will first start with rational numbers:
Rational numbers are those numbers which can be represented as fraction means it has both integer numerator and denominator or which are in the form of a/b where a and b are integers and b can’t be zero. Let’s take some examples of rational numbers:
1. 5 is a rational number because it has 1 in its denominator and can be written as 5/1.
2. 2/3 is also a rational number.
Rational numbers can be added, subtracted, multiplied, divided. These operations are bit typical and given below are some rules to follow for these operations:
Let’s see some operations on How to simplify Rational Numbers:
1. Addition of rational numbers:
While adding two rational numbers, we must take care that the denominators of the rational numbers to be added must be same. If the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.
p/q + r/q = (p + r)/q
2. Subtraction of rational numbers:
While subtracting two rational numbers, we must take care that the denominators of the rational numbers to be subtracted must be same. If the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.
p/q - r/q = (p - r)/q
3. Multiplication of rational numbers:
While multiplying two rational numbers simply multiply the numerators together and then multiply the denominator together and simplify them.
p/q x r/s = (p x r)/(q x s)
4. Division of rational numbers:
While dividing the rational numbers simply take reciprocal of the second fraction and multiply both the rational numbers together.
p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)
Now let’s move to the next topic i.e. numbers:
Numbers can be defined as the unit which is used for counting the objects. Numbers can be categorized in many forms like:
1. Counting numbers = 1, 2, 3, 4, ……
2. Whole numbers = 0, 1, 2, 3, 4, …..
3. Integers = ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
4. Rational numbers = a/b, where ‘a’ and ‘b’ are integer, b is not zero like 2/5.
5. Irrational numbers = Numbers which are not rational like 3.1421.
6. Real numbers = All rational and irrational numbers.
7. Complex numbers = They are combination of real and imaginary numbers like 3 + 2i.
8. Imaginary numbers = Squaring these numbers gives negative real numbers like I = sqrt(-1). Read more for full explanation,
This is all about the rational numbers and numbers, If anybody wants to know How to solve mathematical Expressions
Now we will first start with rational numbers:
Rational numbers are those numbers which can be represented as fraction means it has both integer numerator and denominator or which are in the form of a/b where a and b are integers and b can’t be zero. Let’s take some examples of rational numbers:
1. 5 is a rational number because it has 1 in its denominator and can be written as 5/1.
2. 2/3 is also a rational number.
Rational numbers can be added, subtracted, multiplied, divided. These operations are bit typical and given below are some rules to follow for these operations:
Let’s see some operations on How to simplify Rational Numbers:
1. Addition of rational numbers:
While adding two rational numbers, we must take care that the denominators of the rational numbers to be added must be same. If the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.
p/q + r/q = (p + r)/q
2. Subtraction of rational numbers:
While subtracting two rational numbers, we must take care that the denominators of the rational numbers to be subtracted must be same. If the denominators are not same then find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.
p/q - r/q = (p - r)/q
3. Multiplication of rational numbers:
While multiplying two rational numbers simply multiply the numerators together and then multiply the denominator together and simplify them.
p/q x r/s = (p x r)/(q x s)
4. Division of rational numbers:
While dividing the rational numbers simply take reciprocal of the second fraction and multiply both the rational numbers together.
p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)
Now let’s move to the next topic i.e. numbers:
Numbers can be defined as the unit which is used for counting the objects. Numbers can be categorized in many forms like:
1. Counting numbers = 1, 2, 3, 4, ……
2. Whole numbers = 0, 1, 2, 3, 4, …..
3. Integers = ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
4. Rational numbers = a/b, where ‘a’ and ‘b’ are integer, b is not zero like 2/5.
5. Irrational numbers = Numbers which are not rational like 3.1421.
6. Real numbers = All rational and irrational numbers.
7. Complex numbers = They are combination of real and imaginary numbers like 3 + 2i.
8. Imaginary numbers = Squaring these numbers gives negative real numbers like I = sqrt(-1). Read more for full explanation,
This is all about the rational numbers and numbers, If anybody wants to know How to solve mathematical Expressions
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