BODMAS Rule
Math Formulas
This page consists of formulas of the BODMAS Rule and its application in the questions. Find a solved example of the BODMAS Rule with a detail explanation.
B = Brackets
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
This means while solving arithmetic expressions with multiple operations of various types:
- First, the expressions within the brackets ( (), {}, []) are to be solved irrespective of the operators inside the brackets.
- Next, the square roots and numbers with powers are to be solved. The O in BODMAS stands for Of or Order.
- Then, we must solve the division operation, followed by multiplication, addition, and lastly, subtraction.
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Natural Numbers
This page consists of formulas of Natural Numbers and its application in the questions. Find solved example of Natural Numbers with detail explanation. Natural numbers are the numbers used to count physical things. They start at 1 and go 1,2,3,4,⋯ continuing upward infinitely. We use the symbol N to denote them.
The natural numbers are positive and contain no fractional numbers.
Ascending Order
This page consists of formulas of Ascending Order and its application in the questions. Find solved example of Ascending Order with detail explanation.
Odd Number
This page consists of formulas of Odd Number and its application in the questions. Find solved example of Odd Number with detail explanation. Odd Numbers
An odd number is any integer not divisible by 2.
Example: ...-5, -3, -1, 1, 3, ...
Any odd number may be written as 2n+1
Coprime Numbers
This page consists of formulas of Coprime Numbers and its application in the questions. Find solved example of Coprime Numbers with detail explanation. Coprime Numbers
Co-prime numbers are numbers which have no positive factors in common other than 1
Explanation:co-prime numbers are also sometimes called relatively prime.
As an example:
12 has positive factors: 1,2,3,4,and6 and 35 has positive factors: 1,5,and7 Since the only positive factor 12 and 35 share is 1, they are co-prime.
Find Below pdf consist of formulas and solved example of Coprime Numbers
LCM and HCF
This page consists of formulas of LCM and HCF and its application in the questions. Find solved example of LCM and HCF with detail explanation.
Factors and Multiples: All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. For example, 24 is completely divisible by 1, 2, 3, 4, 6, 8, 12, 24. Each of these numbers is called a factor of 24 and 24 is called a multiple of each of these numbers.
- LCM : The least number which is exactly divisible by each of the given numbers is called the least common multiple of those numbers. For example, consider the numbers 3, 31 and 62 (2 x 31). The LCM of these numbers would be 2 x 3 x 31 = 186.
To find the LCM of the given numbers, we express each number as a product of prime numbers. The product highest power of the prime numbers that appear in prime factorization of any of the numbers gives us the LCM.
For example, consider the numbers 2, 3, 4 (2 x 2), 5, 6 (2 x 3). The LCM of these numbers is 2 x 2 x 3 x 5 = 60. The highest power of 2 comes from prime factorization of 4, the highest power of 3 comes from prime factorization of 3 and prime factorization of 6 and the highest power of 5 comes from prime factorization of 5.
- HCF : The largest number that divides two or more numbers is the highest common factor (HCF) for those numbers. For example, consider the numbers 30 (2 x 3 x 5), 36 (2 x 2 x 3 x 3), 42 (2 x 3 x 7), 45 (3 x 3 x 5). 3 is the largest number that divides each of these numbers, and hence, is the HCF for these numbers. HCF is also known as Greatest Common Divisor (GCD).
To find the HCF of two or more numbers, express each number as product of prime numbers. The product of the least powers of common prime terms gives us the HCF. This is the method we illustrated in the above step.
Also, for finding the HCF of two numbers, we can also proceed by long division method. We divide the larger number by the smaller number (divisor). Now, we divide the divisor by the remainder obtained in the previous stage. We repeat the same procedure until we get zero as the remainder. At that stage, the last divisor would be the required HCF.
Centroid of Triangle
This page consists of formulas of Centroid of Triangle and its application in the questions. Find solved example of Centroid of Triangle with detail explanation. Centroid of Triangle
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.
The centroid is also called the center of gravity of the triangle. If you have a triangle plate, try to balance the plate on your finger. Once you have found the point where it will balance, that is the centroid of that triangle.
Surface Area of a Sphere
This page consists of formulas of Surface Area of a Sphere and its application in the questions. Find solved example of Surface Area of a Sphere with detail explanation. Surface Area of a Sphere
A sphere is a three-dimensional space, such as the shape of a football. A sphere is a body bounded by a surface whose every point is equidistant (i.e. the same distance) from a fixed point, called the centre or the origin of the sphere.
Like a circle in three dimensions, all points from the center are constant. The distance from the center to any points on boundary is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere. One-half of a sphere is called a hemisphere.
Perimeter of a Rectangle
This page consists of formulas of Perimeter of a Rectangle and its application in the questions. Find solved example of Perimeter of a Rectangle with detail explanation. Perimeter of a Rectangle.We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle.
ABCD is a rectangle. We know that the opposite sides of a rectangle are equal.
AB = CD = 5 cm and BC = AD = 3 cm
So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm
Area of a Rectangle
This page consists of formulas of Area of a Rectangle and its application in the questions. Find solved example of Area of a Rectangle with detail explanation.
Area of a Rectangle
To find the area of a rectangle, multiply the length by the width. The formula is:
A = L * W where A is the area, L is the length, W is the width, and * means multiply.
Surface Area of a Cube
This page consists of formulas of Surface Area of a Cube and its application in the questions. Find solved example of Surface Area of a Cube with detail explanation.
Surface Area of a Cube
The area required for making the cube is its surface area. After unfolding it we get the area of each face. The total area of each face which is in square shape gives us the Surface area of cubical shape.