grade 8 number theory

..

We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (3 x 1) + The successive digits ..

The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational numbers Q The set of irrat..

Let the two numbers be x and y. 24 is the mean proportional of x and y x.y=(24) 2 1 192 is the third proportional to x and y. y 3 = (24) 2 .24 x 8 y 3 = (24) 3 .2 3 y=24 x 2=48. \ the numbers are 12 and 48. 7) If a:b::b:c, prove that a:c=a 2 :b ..

T r + 1 in the expansion of Putting r = 8, we get coefficient of Putting r = 9, we get coefficient of ..

Factors of 3a are 1, a, 3, 3a . Divide 3a 3 ,-6a 2 and 3a by 3a, we get HCF is one factor and the quotient is the other factor. ..

Let p(x) = x 3 +ax 2 +bx+12 when p(x) is x-2, R = p(2) = 2 3 +a(2) 2 +b(2)+12 = 8+4a+2b+12 = 20+4a+2b But x-2 is a factor, 20+4a+2b = 0 when p(x) is by x-3, R = p(3) = 27+9a+3b+12 = 39+9a+3b But x-3 is a factor, 39+9a+3b=0 [9a+3b=-39] 3 3a+b = -13 (2) Subtracting equat..

The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 1 = 6, A 2 2 = -2, A 2 3 = -14 A 3 1 = 1, A 3 2 = 5, A ..

4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..

The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b. For example the sub-triplicate ratio of 8a 3 : 27b 6 is or 2a : 3b 2 . Find the compounded ratio of the duplicate ratio of ; sub-triplicate ra..