What are Real numbers?|what are rational and irrational numbers|what are prime numbers? Real number system A real number is a number that can be found on the number line. These are the numbers that we normally use and apply in real-world applications. Below is a diagram of the real number system. Real numbers are mainly classified into rational and irrational numbers. A rational number is a number that can be written as a ratio of two integers. It can be a fraction, an integer, a whole number, or even a natural number.Examples of rational numbers are−523,−18,−4,0,37,9-523,-18 ..read more

1. Mensuration Formulas for RECTANGLEArea of Rectangle = Length × Breadth.Perimeter of a Rectangle = 2 × (Length + Breadth)Length of the Diagonal = √(Length2+ Breadth2) 2. Mensuration Formulas for SQUAREArea of a Square = Length × Length = (Length)2Perimeter of a square = 4 × LengthLength of the Diagonal = √2 × Length 3. Mensuration Formulas for PARALLELOGRAMArea of a Parallelogram = Length × HeightPerimeter of a Parallelogram = 2 × (Length + Breadth) 4. Mensuration Formulas for TRIANGLEArea of a triangle=(1/2)(Base × Height)=(1/2)(BC×AD) For a triangle with sides measuring a, b and c ..read more

(1) (a + b)² = a² + 2 ab + b²(2) (a + b)² = (a - b)² + 4 ab (3) (a - b)² = a² - 2 ab + b²(4) (a - b)² = (a + b)² - 4 ab (5) a² - b² = (a + b) (a - b) (6) (x+a) (x+b) =x² + (a + b) x+a b (7) (a+b)³=a³+3a²b+3ab²+b³(8) (a+b)³=a³+b³+3ab(a+b) (9) (a-b)³=a³-3a²b+3ab²-b³(10) (a-b)³=a³-b³-3ab(a-b) (11)  a³+b³ = (a+b)(a²-ab+b²)(12)  a³+b³=(a+b)³-3 ab(a + b) (13) a³-b³= (a-b)(a²+ab+ b²)(14) a³-b³=(a-b)³ +3ab(a-b) (15) (a+b+c)²= a²+b²+c² +2ab+2bc+2ca(16) (a+b-c)²=a²+b²+c² +2ab-2bc-2ca(17) (a-b+c)²= a²+b²+c²-2ab-2bc+2ca(18) (a-b-c)²= a²+b²+c²-2ab+2bc-2ca(19) a² + b² = (a + b)² - 2ab(20) a² + b ..read more

How to calculate HCF and LCM?|full form of LCM and HCF  HCF The HCF or Highest Common Factor of two or more numbers is the greatest common factor of the given set of numbers. In other words, HCF is the greatest number which exactly divides two or more given numbers. Methods to find HCF By listing factors eg to find the HCF of 4 and 6 List factors of 4 and 6 Factors of 4 are 1,2,4Factors of 6 are 1,2,3,6The highest common factor is 2,clearly. By prime factorisation We have to find prime factors of both the number of which we have to find HCF of 36 and 48 Step 1: Finding prime factors ..read more

PolygonsA polygon is a closed figure where the sides are all line segments. Each side must intersect exactly two others sides but only at their endpoints. The sides must be noncollinear and have a common endpoint.A polygon is usually named after how many sides it has, a polygon with n-sides is called a n-gon. E.g. the building which houses United States Department of Defense is called pentagon since it has 5 sides. Kindle Unlimited Membership Plans Types of PolygonsRegular or IrregularA regular polygon has all angles equal and all sides equal, otherwise it is irregularRegularIrregular Concav ..read more

The branch of mathematics which involves variables as numbers is known as algebra. Kindle Unlimited Membership Plans Rules of Algebra Here, are some of the definition that will give you a better clarity on this: Variables The major point of difference between arithmetic and algebra is the variable. Commonly, the variables are used in the formulas. For example, the area of the triangle is ½ b × h. Here, b represents the base of the triangle and h represents the height of the triangle. ½ used in this formula is a constant. Unlike a variable, a constant is a quantity that remains same throughout ..read more

How to calculate factors and multiples?|difference between factors and multiples? Factors and multiples Factors are what we can multiply to get the numberMultiples are what we get after multiplying the number by an integer (not a fraction).Example: the positive factors, and some multiples, of 6:Factors: 1 × 6 = 6, so 1 and 6 are factors of 62 × 3 = 6, so 2 and 3 are factors of 6 Multiples: 0 × 6 = 0, so 0 is a multiple of 61 × 6 = 6, so 6 is a multiple of 62 × 6 = 12, so 12 is a multiple of 6and so on(Note: there are negative factors and multiples as well)Here are the details:Factors"Fact ..read more

What are the methods to find square root of imperfect square?|how to find square root by long division?| How to find square root by observation?How to manually find a square root1.By long division methodFirst, divide the number to be square-rooted into pairs of digits, starting at the decimal point. That is, no digit pair should straddle a decimal point. (For example, split 1225 into "12 25" rather than "1 22 5"; 6.5536 into "6. 55 36" rather than"6.5 53 6".) Then you can put some lines over each digit pair, and a bar to the left, somewhat as in long division.  +--- ---- ---- | 4 6 ..read more

What is Divisibilty test of 3?|What is Divisibilty test of 4?|What is Divisibilty test of  7?|What is Divisibilty test of 8?|What is Divisibilty test of 9? Divisibility TestsThe following are some shortcuts for deciding whether a given integer is divisible by2,3,4,5,6,8,9  .Divisibility by  2An integer is divisible by  2 if its last digit  0,2,4,6 or  8 . (In other words, if it's even.)Example: 24,424,5286,19578...... .Divisibility by  3An integer is divisible by  3 if the sum of its digits is divisible by  3 .Example: 81 as 8+1 =9 and 9 is divisible by 3 Divisibility by 4  An integer is di ..read more

Vedic method to multiply 2 digit numbers:To multiply two 2-digit numbers without showing work,   first multiply the ones digits together, then 'cross-multiply,' and finally multiply the tens digitstogether. Make sure to carry whenever a product exceeds 9. As you will see in the examples below, you must work your way from right to left to perform this trick Vedic method to multiply 3 digit number: 1Draw a table with a x b number of columns and rows, respectively. The number a corresponds ot the number of digits of the multiplicand (number being multiplied) and b to the digits of the multip ..read more