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We will discuss here how to solve the word problems on division of decimal fractions. To divide a decimal number: (i) Perform the division ignoring decimal point. (ii) Put the decimal point in the

Continue reading "Problems on Division of Decimal Fractions | Divide a Decimal Number Problems"

We will discuss here how to solve the word problems on multiplication of decimal fractions. To multiply a decimal number: (i) Perform the multiplication ignoring decimal point. (ii) Place the decimal

Continue reading "Problems on Multiplication of Decimal Fractions | Multiply a Decimal Number"

We will discuss here how to solve the word problems on subtraction of decimal fractions. We know to subtract one decimal number from the other decimal number: (i) Change the decimal fractions to

Continue reading "Problems on Subtraction of Decimal Fractions | Like Decimal Fractions"

We will discuss here how to solve the word problems on addition of decimal fractions. We know to add two or more decimals: (i) Convert all the decimals to be added into like decimals.

Continue reading "Problems on Addition of Decimal Fractions | Add Two or more Decimals"

We will discuss about the equality of complex numbers. Two complex numbers z1 = a + ib and z2 = x +iy are equal if and only if a = x and b = y i.e., Re (z1) = Re (z2) and Im (z1) = Im (z2).

Continue reading "Equality of Complex Numbers | Equality of Two Complex Numbers | Examples"

Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

Continue reading "Decimal Place Value Chart |Tenths Place | Hundredths Place | Thousandths Place"

We will discuss here about changing unlike to like decimal fractions. Unlike decimal fractions can be changed to like decimals by adding as many zeroes as required.

Continue reading "Changing Unlike to Like Decimal Fraction | Like and Unlike Decimals | examples"

We will discuss here about the expanded form of decimal fractions. In expanded form of decimal fractions we will learn how to read and write the decimal numbers.

Continue reading "Expanded form of Decimal Fractions | How to Write a Decimal in Expanded Form"

To find the Amplitude or Argument of a complex number let us assume that, a complex number z = x + iy where x > 0 and y > 0 are real, i = √-1 and x\(^{2}\) + y\(^{2}\) ≠ 0

Continue reading "Amplitude or Argument of a Complex Number | Algorithm for Finding Argument"

A fractional number whose denominator is 10 or multiple of 10 is called a decimal. Every decimal has two parts whole number part and decimal part. These two parts are separated by a dot or point.

Continue reading "Decimal | Word Problem on Decimals | Digits after the Decimal | Fraction"

In ordering decimals we will learn how to compare two or more decimals. (i) Convert each of them as like decimals. (ii) Compare these decimals just as we compare two whole numbers ignoring

Continue reading "Ordering Decimals | Comparing Decimals | Decimals from Smallest to Largest"

We will learn step-by-step how to solve different types of problems on complex numbers using the formulas. 1. Express \((\frac{1 + i}{1 - i})^{3}\) in the form A + iB where A and B are real numbers.

Continue reading "Problems on Complex Numbers | Modulus of the Complex Quantity"

We will discuss about the complex numbers formulae. (i) Definition of complex number: If an ordered pair (x, y) of two real numbers x and y is represented by the symbol x + iy, where i = √-1, then the

Continue reading "Complex Numbers Formulae | Properties of Complex Numbers | Definition"

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"

We will practice the questions given in the worksheet on division of a whole number by a fraction. We know, whole number ÷ fraction = whole number × reciprocal of fraction.

Continue reading "Worksheet on Division of a Whole Number by a Fraction | Reciprocal of Fraction"

We will discuss here about the cube roots of unity and their properties. Suppose let us assume that the cube root of 1 is z i.e., ∛1 = z.Then, cubing both sides we get, z^3 = 1 or, z^3 - 1 = 0

Continue reading "The Cube Roots of Unity | Properties of the Cube roots of Unity |Complex Numbers"

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 practice the questions given in the worksheet on problems on division of fractional numbers. 1. A student in a school pays $ 3 1/5 as boys fund. If the amount collected is $ 310 2/5

Continue reading "Worksheet on Problems on Division of Fractional Numbers | Fractional Division"

We will learn how to expand a complex in the standard form a + ib. The following steps will help us to express a complex number in the standard form: Step I: Obtain the complex number in the form

Continue reading "Complex Number in the Standard Form | Multiply the Conjugate of the Denominator"

We will practice the questions given in the worksheet on division of a fraction by a whole number. We know, fraction ÷ whole number = fraction × reciprocal of whole number. I. Divide the following:

Continue reading "Worksheet on Division of a Fraction by a Whole Number | Find the Quotient"

We will practice the questions given in the worksheet on division of a fractional number by a fractional number. We know, a fraction ÷ another fraction = first fraction × reciprocal of the

Continue reading "Worksheet on Division of a Fractional Number by a Fractional Number | Answers"

How to find the reciprocal of a complex number? Let z = x + iy be a non-zero complex number. Then 1/z = 1/(x + iy) Multiplying numerator and denominator by conjugate of denominator

Continue reading "Reciprocal of a Complex Number | How to Find the Reciprocal of a Complex Number?"

Problems on division of fractional numbers will give idea how to solve different types of word problems. 1. In a school 2/7 of the students are girls. If there are 280 boys

Continue reading "Problems on Division of Fractional Numbers | Fractional Division | Word Problems"

Here we will discuss about the associative property of multiplication of complex numbers. Commutative property of multiplication complex numbers: For any three complex numbers z1, z2 and z3, we have

Continue reading "Associative Property of Multiplication of Complex Numbers | Complex Numbers"

Here we will discuss about the commutative property of multiplication of complex numbers. Commutative property of multiplication of two complex numbers: For any two complex number z1 and z2, we have

Continue reading "Commutative Property of Multiplication of Complex Numbers | Complex Numbers"

In simplification of fractions parenthesis can also be used. The three parenthesis (1st), {2nd}, [3rd] are used commonly. Examples on simplification of fractions:

Continue reading "Simplification of Fractions | How to Simplify Fraction? | reducing fractions"

In the worksheet on division of fractions we will solve 10 different types of questions. 1. Solve: (a) 3/5 ÷ 5 (b) 2/15 ÷ 6 (c) 49/6 ÷ 35 (d) 13 1/7 ÷ 7

Continue reading "Worksheet on Division of Fractions | Problems on Division of Fraction"

Properties of fractional division are discussed here: (i) When a fractional number is divided by 1, the quotient is the fraction itself. For Example: 1. 2/3 ÷ 1 = 2/3 × 1/1 = (2 × 1)/(3 × 1) = 2/3

Continue reading "Properties of Fractional Division | Dividing Fractions | Fraction Division"

We will discuss here about the different properties of complex numbers. 1. When a, b are real numbers and a + ib = 0 then a = 0, b = 0 Proof: According to the property, a + ib = 0 = 0 + i * 0,

Continue reading "Properties of Complex Numbers |Equality of Two Complex Numbers|Distributive Laws"

Integral power of a complex number is also a complex number. In other words any integral power of a complex number can be expressed in the form of A + iB, where A and B are real.

Continue reading "Integral Powers of a Complex Number | Integral Power of i | Complex Number"

We will discuss here about division of a fractional number by a fractional number. A Fraction ÷ Another Fraction = First Fraction × Reciprocal of the Second Fraction.

Continue reading "Division of a Fractional Number | Reciprocal of the Second Fraction"

In division of a whole number by a fraction the rules are: Whole Number ÷ Fraction = Whole Number × Reciprocal of Fraction.

Continue reading "Division of a Whole Number by a Fraction | Division of Fraction"

We will discuss here about division of a fraction by a whole number. Fraction ÷ Whole number = Fraction × Reciprocal of whole number.

Continue reading "Division of a Fraction by a Whole Number | Division of Fractions | Fractions"

Root of a complex number can be expressed in the standard form A + iB, where A and B are real. In words we can say that any root of a complex number is a complex number Let, z = x + iy

Continue reading "Root of a Complex Number | Purely Real Quantity | Purely Imaginary Quantity"

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"

Division of complex numbers is also a complex number. In other words, the division of two complex numbers can be expressed in the standard form A + iB where A and B are real.

Continue reading "Division of Complex Numbers | Quotient of Two Complex Numbers"

We will practice the questions given in the worksheet on problems on multiplication of fractional numbers. 1. The cost of an electric bulb is $ 6 ½. Find the cost of 50 such bulbs.

Continue reading "Worksheet on Problems on Multiplication of Fractional Numbers | Answers"

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

Continue reading "Word Problems on Fraction | Math Fraction Word Problems | Fraction Math"

Problems on multiplication of fractional numbers will give idea how to solve different types of word problems. 2. One meter of cloth costs $ 15 1/2. Find the cost of 14 1/2 meter of cloth.

Continue reading "Problems on Multiplication of Fractional Numbers | Multiplying Fractions"

Multiplication of two complex numbers is also a complex number. In other words, the product of two complex numbers can be expressed in the standard form A + iB where A and B are real.

Continue reading "Multiplication of Two Complex Numbers | Product of Two Complex Numbers "

We will practice the questions given in the worksheet on multiplicative inverse of a fractional number. We know, to get the reciprocal of a given fraction, we interchange the numerator

Continue reading "Worksheet on Multiplicative Inverse |Multiplicative Inverse of Fractional Number"

Using the properties of multiplication we will solve the different questions given in the worksheet on properties of multiplication of fractional numbers.

Continue reading "Worksheet on Properties of Multiplication of Fractional Numbers | Answers"

In worksheet on multiplication on fraction, we can see below there are 10 different types of questions which we can practice in our homework.

Continue reading "Worksheet on Multiplication on Fraction | Properties of Fraction Multiplication"

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"

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"

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