Question

class VIIl
maths.
ch: 1, 2, 3, 4,5,6,7 all formulas​

Answer 1

Answer:

Any number that can be written in the form of p ⁄ q where q ≠ 0 are rational numbers. It posses the properties of:

Additive Identity: (a ⁄ b + 0) = (a ⁄ b)

Multiplicative Identity: (a ⁄ b) × 1 = (a/b)

Multiplicative Inverse: (a ⁄ b) × (b/a) = 1

Closure Property – Addition: For any two rational numbers a and b, a + b is also a rational number.

Closure Property – Subtraction: For any two rational numbers a and b, a – b is also a rational number.

Closure Property – Multiplication: For any two rational numbers a and b, a × b is also a rational number.

Closure Property – Division: Rational numbers are not closed under division.

Commutative Property – Addition: For any rational numbers a and b, a + b = b + a.

Commutative Property – Subtraction: For any rational numbers a and b, a – b ≠ b – a.

Commutative Property – Multiplication: For any rational numbers a and b, (a x b) = (b x a).

Commutative Property – Division: For any rational numbers a and b, (a/b) ≠ (b/a).

Associative Property – Addition: For any rational numbers a, b, and c, (a + b) + c = a + (b + c).

Associative Property – Subtraction: For any rational numbers a, b, and c, (a – b) – c ≠ a – (b – c)

Associative Property – Multiplication: For any rational number a, b, and c, (a x b) x c = a x (b x c).

Associative Property – Division: For any rational numbers a, b, and c, (a / b) / c ≠ a / (b / c) .

Distributive Property: For any three rational numbers a, b and c, a × ( b + c ) = (a × b) +( a × c).

Laws of Exponents

a0 = 1

a-m = 1/am

(am)n = amn

am / an = am-n

am x bm = (ab)m

am / bm = (a/b)m

(a/b)-m =(b/a)m

(1)n= 1 for infinite values of n.

a) Linear Equations in One Variable: A linear equation in one variable has the maximum one variable of order 1. It is depicted in the form of ax + b = 0, where x is the variable.

b) Linear Equations in Two Variables: A linear equation in two variables has the maximum of two variables of order 2. It is depicted in the form of ax2 + bx + c = 0.

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

(a + b) (a – b) = a2 – b2

(x + a) (x + b) = x2 + (a + b)x + ab

(x + a) (x – b) = x2 + (a – b)x – ab

(x – a) (x + b) = x2 + (b – a)x – ab

(x – a) (x – b) = x2 – (a + b)x + ab

(a + b)3 = a3 + b3 + 3ab(a + b)

(a – b)3 = a3 – b3 – 3ab(a – b)

Square & Square Roots

If a natural number, m = n2 and n is a natural number, then m is said to be a square number.

Every square number surely ends with 0, 1, 4, 5 6 and 9 at its units place.

A square root is the inverse operation of the square.

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