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Mathematics might seem like a tough subject to crack. However, if the students focus more on the concepts, learn all the necessary formulas, and practice enough, the fear of the subject could be avoided. The Class 6 Mathematics covers a variety of topics such as Number Systems, Integers, Decimals, Fractions, Mensuration, Algebra, and Ratio and Proportion. Remembering the formulas for these topics can really help students in their preparation for the mathematics examination. In this article, we will look at a set of basic Maths formulae to master the foundations of Class 6 Mathematics. Instead of just memorizing an equation, students will discover how to apply the concepts to reach the final answer.
| Table of Content |
Key Terms: Geometry, mensuration, algebra, number system, integers
Imprtant Formula for Class 6
[Click Here for Sample Questions]
The important formulas for all chapters of Class 6 Mathematics are as follows:
Also Read:
Number System Formulas
The important formulas for the Class 6 Mathematics, Number System is as tabulated below:
| \(\sqrt{ab} = \sqrt{a}\sqrt{b}\) |
| \(\sqrt{\frac{a}{b}} ={\frac{\sqrt{a}}{\sqrt{b}}}\) |
| \((\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a-b\) |
| \((\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a^2-b\) |
| \((\sqrt{a} + \sqrt{b})^2 = a-2 \sqrt{ab} + b\) |
| apaq = ap+q |
| (ap)q=apq |
| ap/aq= ap−q |
| apbp = (ab)p |
| If a and b are integers, then in order to rationalize the denominator of \(\frac{1}{\sqrt{a} + b}\), multiply this by \(\frac{\sqrt{a} - b}{\sqrt{a} - b}\) |
| Integer Properties: For any given integers a and b, |
| The addition of integers is commutative, i.e. a + b = b + a |
| The addition of integers is associative, i.e. a + (b + c) = (a + b) + c |
| Under addition, 0 is the identity element i.e. a + 0 = 0 + a = a |
| Multiplication of integers is commutative in nature i.e. a x b = b x a |
| The identity element under multiplication is 1, i.e. 1 x a = a x 1 = a |
Also Read: Real Numbers Formula
Mensuration Formulas for Two dimensional Figures
| 2-D Figures | Area in Square Units | Perimeter in Units |
|---|---|---|
| Square | (side)2 | 4 x side |
| Triangle | ½ ( bxh ) | Sum of all sides |
| Rectangle | length x breadth | 2.(l+b) |
| Circle | πr2 | 2πr |
Basic Algebra Formula
Consider the simple quadratic equation ax2+bx+c = 0
Herein, the coefficient of x2 is a
the coefficient of x is b
and c is a constant term
The quadratic formula to find the variable x, therefore, is
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
Ratio and Proportion Formula
The ratio of any number ‘a’ to another number ‘b’ (where b ≠ 0) is the fraction a/b. It is written as a:b.
- The ratio of any two numbers is always expressed in the simplest form.
For example, 12/8 will be expressed as 3/2.
- An equality ratio is referred to as the proportion in such a way that a:b = c:d only if ad = bc.
- If a:b = b:c, then we can say that a, b and c are in a continued proportion.
- If a, b and c are in continued proportion, then a:b::b:c, then b will be represented as the mean proportional between the constants a and c.
- The value of one article is equal to the value of a given number of articles divided by the number of articles (Unitary Method).
The more the number of articles here, the more is the resulting value and vice-versa.
Also Read:
| Prime Number | Roman Number |
| Difference between place value and face value | Natural numbers and Whole numbers |
Things to Remember
- Students must make a habit of remembering the formulas through writing.
- It is advised to write the formulas on a sheet of paper and stick it on your wall.
- The ratio of two numbers is always expressed in their simplest form. For example, 6/8 will be further reduced to 3/4.
- Through the unitary method, the value of one article is equal to the value of a given number of articles divided by the number of articles.
- The quadratic formula to find the variable x is \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
- The addition of integers is commutative, i.e. a + b = b + a.
- The addition of integers is associative, i.e. a + (b + c) = (a + b) + c
- A quadrilateral is a four-sided polygon.
- An important formula of the number system is \((\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a-b\)
Sample Questions
Ques. State the important properties of proportion? (5 marks)
Ans. The following are the important properties of proportion:
- Addendo: If a:b = c:d, then we can say that (a + c):(b + d)
- Subtrahend: If a:b = c:d, then it can be demonstrated that a – c:b – d
- Dividendo: If a:b = c:d, then we get a–b:b = c–d:d
- Componendo: If a:b = c:d, then we get a+b:b = c+d :d
- Alternendo: If a:b = c:d, then a:c = b:d
- Invertendo: If a:b = c:d, then we can say that b:a = d:c.
- Componendo and dividendo: If a:b = c:d, then we get a+b:a–b = c+d:c – d
Ques. What are the properties of Natural Numbers and Whole Numbers? (5 marks)
Ans. The various properties of Natural numbers and Whole numbers are as follows:
Addition Property
- When any two natural numbers are added, the result we get is a natural number.
Eg: 44+145 = 189
- In a similar way, when any two or more whole numbers are added, the result we get is a whole number.
Eg: 6+11= 17
Subtraction Property
- The subtraction of any two natural numbers either will or will not result in a natural number.
Eg: 6 –12 = -6 is not natural number
But 10 – 5 = 5 is a natural number
- The subtraction of any two whole numbers may or may not result in any whole number.
Multiplication Property
- The multiplication of any two natural numbers will always result in a natural number.
Eg: 12 x 5 = 60 is a natural number
- The multiplication of any two whole numbers always do result in a whole number
Eg: 12 x 0 = is a whole number, where 2 and 0 are also whole numbers.
Division Property
- Division of any two natural numbers may not always result in a natural number.
- Division of any two whole numbers may not always result in a whole number.
This is because if the result is in fraction or decimal, then they are not considered as natural or whole numbers.
E.g., 4/2 = 2 is natural as well as the whole number.
But 5/2 = 2.5 is neither natural nor the whole number.
Ques. What are the important formulas of mensuration? (3 marks)
Ans. Some important formulas of mensuration are as follows:
- Square- The area of square is (side)2 and the perimeter is 4 x side.
- Triangle: The area of triangle is ½(b x h) and its perimeter is the sum of all sides.
- Rectangle: The area of the rectangle is length x breadth while the Perimeter is 2*(length + breadth).
- Circle: The area of the circle is πr2 while its perimeter is 2πr.
Ques. What is the order of operations in algebra? (5 marks)
Ans. The order of operation in algebra is given as follows:
- The preference is first given to all operations that exist inside the brackets.
- All the operations on exponents and roots then must be performed.
- This step is then followed by the division and multiplication operations that move from the left to right.
- After that, all the addition and subtraction operations should be performed in an order from left to right.
Ques. Write a basic algebra formula. (3 marks)
Ans. Consider the simple quadratic equation ax2+bx+c = 0
Herein, the coefficient of x2 is a
the coefficient of x is b
and c is a constant term
The quadratic formula to find the variable x, therefore, is
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
Ques. Write the Division Property. (5 marks)
Ans. The division property is as follows:
- Division of two natural numbers may not always result in a natural number.
- Division of two whole numbers may not always result in a whole number.
Now, this is because if the results of the division is in decimal or fraction, then they aren’t considered as whole or natural numbers.
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