Ayush Agarwal Maths

Percentage -   According to mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted by using the percent sign, "%" .  Percentage formula -  Percentage = (Obtained marks/Total                                marks)×100 Example :-  3/5 ×100 = 0.60×100 = 60% =                                  60percent About Percentage - 1. 10% is equal to 1/10 fraction 2.  20% is equivalent to ⅕ fraction 3.  25% is equivalent to ¼ fraction 4.  50% is equivalent to ½ fraction 5.  75% is equivalent to ¾ fraction 6.  90% is equivalent to 9/10 fraction Points to remember :- 1. A percentage is a dimensionless number, it has no unit of measurement.  Practice Questions - Q1.   Convert as a fraction and as a decimal :   40% Q2. Express the ratio 4:5 as a percentage. Q3. Find 30% of ₹800. Q4. If 10% of a number is 45, then find the number? Thank you for visiting  Keep sharing  Join us now :-  Instagram

Factorisation - The process of finding two or more expressions whose product is the given expression is called factorisarion. 

Algebra-  Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.  ALGEBRAIC EXPRESSIONS- A combination of constants and variables, connected by some or all of the operations +, -, ×, and  ÷ is known as an algebraic expression.                          Polynomials  Monomial  - Polynomial having one term.  Binomial  - Polynomial having two terms.  Trinomial  - Polynomial having three terms Zero Polynomial  - Polynomial having all its coefficient zero.  Constant Polynomial  - A polynomial having only a single term ( of real number).  Standard form  - Powers of x are either in increasing or decreasing order.  Addition of Algebraic expressions - In the addition of algebraic expression we collect the like terms and add them.  Practice Questions  1. Solve the following equation for P  : 2P/3 = 8 + 4P 2.If 8x + 5x + 2x + 4x = 114, then 7x + 8 = ?  3. If a = 3, then a 3 (a 3 -a)= ?  4. 5x + 2(x + 7) = 14x – 7. Find x ?  5. 

Rational numbers :- The numbers of the form p/q , where p and q are integers and q is not equal to zero, q≠ 0 , are called rational numbers.  0 is neither positive nor negative.  Example-  Numbers 3/5 , -1/14 is a rational number.  - Every integer is a rational number.  - Every whole number is a rational number because every whole number can be expressed as a fraction. Positive rationals - A rational number is said to be positive if its numerator and denominator are either both positive or both negative.  Example - 3/7 or -6/11 are positive rationals.  Negative rationals - A rational number is said to be negative if its numerator and denominator are of opposite signs.  Example- -7/9, 4/-11 are negative rationals.  Some important facts :- 1. The product of a rational number and its reciprocal is 1. 2.  Zero '0' has no reciprocal.  3. The reciprocal of a positive rational number is positive.  4. The reciprocal of a negative rational number is negative.  5. Every natural number N

                   CUBES AND CUBE ROOTS Cube number- A cube number is a number multiplied by itself twice, or we can say the cube of a number m is its third power.  For example- m³ =  m  ×  m 2  =  m  ×  m  ×  m . 8³ = 8 × 8 2  = 8  × 8  × 8 = 512 .  15³ = 15  ×  15 2  =  15  ×  15  ×  15 = 3375 .   Perfect cube - A natural number is said to be a perfect cube if it is the cube of some natural numbers.  Examples-   1 ³ = 1, 2³ = 8, 3³ = 27, 4³ = 64,  etc.            Thus 1, 8, 27, 64 etc.., are perfect cubes.  Facts About cube numbers:- 1. The cube of a number is that number raised to the power 3 .  2. The cube of an even natural number is even.  3. The cube of an odd natural number is odd.  4.  Numbers ending in 1, 2, 3, 4, 6, 7, 8, 9, 000, 125, 375, 625 or 875 may be cube numbers.  Practice Questions 1. Find the cube of 21 .  2. Find the least number by which 750 should be multiplied, so that it becomes a perfect cube. 3. Solve :- (i) ∛4096  (ii) ∛(729/1000 ) 4. By w