numbers and numerators

\ A + B = B + A \ A + B = B ..

Consider the GP a, ar, ar 2 ... ..

Sum to infinity exists only when r is numerically less than 1. i.e. |r|<..

If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..

(a) (b) Hence we state the classical definition of rational numbers: Find a rational number between two rational numbers To obtain the required number, add numerators and denominators as shown below: ..

If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all approximately zer..

1. Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. 2. If two ratios are equal, we get four quantities in proportion.. 3. If three quantities are in ..

Constants and variables Symbols having fixed values are called constants. Examples: 5, π, ¾, 1.5. Symbols which can be assigned with various numerical values are called variables or literals. Examples : x, y, y 2 . In the formula for circumference of a circle, c=2π..

The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In these examples, study the relation between the middle and the last terms. Therefore, to factorise expressions of the type (x 2 + cx + d), we have to find two ..

Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ratio, sub..