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We will discuss here about the usual mathematical operation - subtraction of two complex numbers. How do you subtract Complex Numbers? Let z1 = p + iq and z2 = r + is be any two complex numbers

Continue reading "Subtraction of Complex Numbers | Difference between Two Complex Numbers"

We will practice the questions given in the worksheet on multiplication of a whole number by a fraction. We know to multiply a whole number by a fraction we multiply the top number of the fraction by

Continue reading "Worksheet on Multiplication of a Whole Number by a Fraction | Answers"

We will practice the questions given in the worksheet on multiplication of a fraction by fraction. We know to multiply a fractional number we need to multiply the numerator of the first fraction

Continue reading "Worksheet on Multiplication of a Fraction by Fraction | Fractional Number"

We will practice the questions given in the worksheet on multiplication of fractional number by a whole number. We know to multiply a fraction by a whole number, the numerator of the fraction

Continue reading "Worksheet on Multiplication of Fractional Number by a Whole Number"

5th grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students.

Continue reading "5th Grade Math Worksheets | 5th Grade Homework Sheets | Math Worksheet"

We will discuss here about the usual mathematical operation - addition of two complex numbers. Let z1 = p + iq and z2 = r + is be any two complex numbers, then their sum z1 + z2 is defined as

Continue reading "Addition of Two Complex Numbers | Algebra of Complex Numbers | Complex Numbers"

We know multiplication is repeated addition. Consider the following: (i) Andrea made sandwiches for 12 people. When they shared it equally, each of them got 1/2 a sandwich. How many sandwiches did

Continue reading "Multiplication is Repeated Addition | Multiplication | Repeated Addition"

If the product of two numbers is 1, then each number is known as multiplicative inverse or the reciprocal of one another. The following are the rules of multiplicative inverse of a fractional number:

Continue reading "Multiplicative Inverse | Reciprocal of a Proper Fraction, an Improper Fraction"

The properties of multiplication of fractional numbers are discussed here. Property 1: If two fractional numbers are multiplied in either order, the product remains the same. For Example:

Continue reading "Properties of Multiplication of Fractional Numbers | Fractional Numbers"

Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:

Continue reading "Divisible by 10 | Test of Divisibility by 10 | Rules of Divisibility by 10"

Divisible by 9 is discussed below: A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9

Continue reading "Divisible by 9 | Test of Divisibility by 9 | Rules of Divisibility by 9"

Divisible by 8 is discussed below: A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8. Consider the following numbers which are divisible by 8

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Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be

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Divisible by 6 is discussed below: A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42

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Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by

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A number is divisible by 4 if the number is formed by its digits in ten’s place and unit’s place (i.e. the last two digits on its extreme right side) is divisible by 4.

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A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Consider the following numbers to find whether the numbers are divisible or not divisible by 3

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A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

Continue reading "Divisible by 2 | Test of Divisibility by 2 | Rules of Divisibility by 2"

In multiplication of fractional number by a whole number the rules are: (a) If the fraction is a mixed fraction, convert it to improper fraction. (c) Always write the answer as a mixed fraction if it

Continue reading "Multiplication of Fractional Number by a Whole Number | Fraction Multiplication"

We will discuss here about the multiplication of a whole number by a fraction. Now let us learn the multiplication of fractional numbers. Let us suppose 6 is multiplied by 1/3

Continue reading "Multiplication of a Whole Number by a Fraction | Fractional Multiplication"

We will discuss here about the multiplication of a fraction by a fraction. 1/2 is multiplied by 1/3 or, 1/3 of 1/2 Suppose this is whole (1)

Continue reading "Multiplication of a Fraction by a Fraction | Multiplication of a Fraction"

Definition of Modulus of a Complex Number: Let z = x + iy where x and y are real and i = √-1. Then the non negative square root of (x^2 + y^2) is called the modulus or absolute value of z (or x + iy).

Continue reading "Modulus of a Complex Number | Absolute Value of a Complex Number"

Definition of conjugate complex numbers: In any two complex numbers, if only the sign of the imaginary part differ then, they are known as complex conjugate of each other.

Continue reading "Conjugate Complex Numbers | Properties of Conjugate of a Complex Number"

The introduction of complex numbers plays a very important role in the theory of numbers. The equations x^2 + 5 = 0, x^2 + 10 = 0, x^2 = -1 are not solvable in the real number system

Continue reading "Introduction of Complex Numbers | concept of imaginary numbers | Examples"

We will solve different types of problems on quadratic equation using quadratic formula and by method of completing the squares. We know the general form of the quadratic equation

Continue reading "Problems on Quadratic Equation | Method of Completing the Squares"

To find the highest common factor of three numbers by using division method is discussed here step by step. Step I: First of all find the highest common factor (H.C.F) of any two

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We will learn step-by-step with the help of examples to find highest common factor of two numbers by using division method.

Continue reading "Examples to find Highest Common Factor of Two Numbers by using Division Method"

We will learn how to find the maximum and minimum values of the quadratic Expression ax^2 + bx + c (a ≠ 0). When we find the maximum value and the minimum value of ax^2 + bx + c then let us assume y

Continue reading "Maximum and Minimum Values of the Quadratic Expression | Greatest & Least Values"

We already acquainted with the general form of quadratic expression ax^2 + bx + c now we will discuss about the sign of the quadratic expression ax^2 + bx + c = 0 (a ≠ 0). When x be real then

Continue reading "Sign of the Quadratic Expression | Quadratic Equation | Discriminant"

We will solve different types of problems given in the Worksheet on H.C.F. and L.C.M. I. Find highest common factor of the following by complete factorisation: (i) 48, 56, 72 (ii) 198, 360

Continue reading "Worksheet on H.C.F. and L.C.M. | H.C.F. by Long Division Method | Answers"

The theory of quadratic equation formulae will help us to solve different types of problems on quadratic equation. The general form of a quadratic equation is ax\(^{2}\) + bx + c = 0

Continue reading "Theory of Quadratic Equation Formulae | Discriminant of a quadratic equation "

In worksheet on word problems on H.C.F. and L.C.M. we will find the greatest common factor of two or more numbers and the least common multiple of two or more numbers and their word problems.

Continue reading "Worksheet on word problems on H.C.F. and L.C.M. | Highest Common Factor | LCM"

We will discuss how to derive the conditions for common root or roots of quadratic equations that can be two or more. Condition for one common root:

Continue reading "Condition for Common Root or Roots of Quadratic Equations | One Common Root"

Let α and β be the roots of the quadratic equation ax^2 + bx + c = 0, (a ≠ 0), then the expressions of the form α + β, αβ, α^2 + β^2, α^2 - β^2, 1/α^2 + 1/β^2 etc. are known as functions

Continue reading "Symmetric Functions of Roots of a Quadratic Equation | Quadratic Equation"

Here we will get the idea how to solve the word problems on H.C.F and L.C.M. 1. Find the smallest number which on adding 19 to it is exactly divisible by 28, 36 and 45. First we find the least

Continue reading "Word problems on H.C.F. and L.C.M. |Least Common Multiple| Highest Common Factor"

We will discuss about the irrational roots of a quadratic equation. In a quadratic equation with rational coefficients has a irrational or surd root α + √β, where α and β are rational and β is not

Continue reading "Irrational Roots of a Quadratic Equation | Surd Roots of a Quadratic Equation"

We will discuss about the complex roots of a quadratic equation. In other words, in a quadratic equation with real coefficients has a complex root α + iβ then it has also the

Continue reading "Complex Roots of a Quadratic Equation | Imaginary Roots of a Quadratic Equation"

We will discuss here about the different cases of discriminant to understand the nature of the roots of a quadratic equation.

Continue reading "Nature of the Roots of a Quadratic Equation | Discuss the Nature of the Roots"

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number.

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To find Least Common Multiple by using Division Method we need to follow the following steps.

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We will learn the relationship between H.C.F. and L.C.M. of two numbers. First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3. Then we need to find the lowest common

Continue reading "Relationship between H.C.F. and L.C.M. | Highest common Factor | Solved Examples"

We will learn the formation of the quadratic equation whose roots are given. To form a quadratic equation, let α and β be the two roots. Let us assume that the required equation be ax^2 + bx + c = 0

Continue reading "Formation of the Quadratic Equation whose Roots are Given | Quadratic Equation"

We will discuss here that a quadratic equation cannot have more than two roots. Proof: Let us assumed that α, β and γ be three distinct roots of the quadratic equation of the general form

Continue reading "Quadratic Equation cannot have more than Two Roots | Quadratic Equation"

We will learn how to find the relation between roots and coefficients of a quadratic equation. Let us take the quadratic equation of the general form ax^2 + bx + c = 0 where a (≠ 0) is the

Continue reading "Relation between Roots and Coefficients of a Quadratic Equation | Examples"

We will discuss that a quadratic equation has only two roots or in other words we can say that a quadratic equation cannot have more than two roots. We will prove this one-by-one.

Continue reading "Quadratic Equation has Only Two Roots | General Form of Quadratic Equation"

We will discuss about the factor theory of quadratic equation. Suppose when we assume that β be a root of the quadratic equation ax^2 + bx + c = 0, then we get (x - β) is a factor of the quadratic

Continue reading "Factor Theory of Quadratic Equation | Quadratic Expression|Roots of the Equation"

Problems on divisibility rules will help us to learn how to use the rules to test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. 1. Is 7248 is divisible (i) by 4, (ii) by 2 and (iii) by 8?

Continue reading "Problems on Divisibility Rules | Rules to Test of Divisibility | Divisible by 4"

Worksheet on divisibility rules will help us to practice different types of questions on test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to

Continue reading "Worksheet on Divisibility Rules | Questions on Test of Divisibility | "

We will discuss about the introduction of quadratic equation. A polynomial of second degree is generally called a quadratic polynomial. If f(x) is a quadratic polynomial, then f(x) = 0 is called

Continue reading "Introduction of Quadratic Equation | Quadratic Polynomial | General Form"

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