Learning all the fundamental principles of CBSE Class 8 Maths is very imperative. If students are serious about scoring high marks in the higher grades, then CBSE Class 8 Maths Practice Worksheets and Question Papers are beneficial for you. There are numerous advantages that Class 8 Maths Students can experience by studying maths with the help of these Worksheets, Practice papers and Multiple Choice Questions . To start with, one can practice each topic and questions by following a extensive detailed and stepwise approach. Moreover, Students gets to practice each chapter and gauge their understanding of a particular topic by attempting various types of questions present in worksheets and practice papers.
A number that can be expressed in the form p/q, where p and q are integers and q≠0.
All integers and all fractions are rational numbers.
A rational number is said to be in its standard form if its denominator is positive and its denominator and numerator are prime to each other.
0 is also a rational number, but it is neither positive nor a negative rational number.
Rational numbers are closed under addition, subtraction, multiplication and division (provided divisor is not 0).
The commutativity of addition as well as that of multiplication is true for rational numbers i.e. if a/b and c/d are any two rational numbers, then a/b + c/d = c/d + a/b and a/b × c/d = c/d × a/b
The associativity of addition is true for rational numbers i.e. is a/b, c/d and e/f are any three rational numbers, then (a/b +c/d) + e/f = a/b + (c/d + e/f)
Subtraction is neither commutative nor associative for rational numbers.
Commutativity and associativity of division is not true for rational numbers.
The sum of 0 and any rational number is the rational number itself i.e. if a/b is any rational number, then a/b + 0 = a/b.
The result of subtracting zero from a rational number is the rational number itself i.e. is a/b is a rational number, then a/b – 0 = a/b.
The negative of a rational number p/q is –p/q.
P/q and –p/q are called negative (or additive inverse) of each other.
Zero is the identity element for addition of rational numbers.
The product of 1 and any rational number is the rational number itself i.e. if p/q is a rational number, then p/q × 1 = p/q
The product of 0 and any rational number is 0 i.e. p/q × 0 = 0.
If a/b and c/d are two rational numbers such that a/b × c/d = 1, then each is called the multiplicative inverse or reciprocal of each other.
Zero has no reciprocal.
We can get countless rational numbers between any two given rational numbers.
If x and y are two rational numbers, then (x + y)/2 is a rational number between x and y such that x < (x + y)/2 < y.
Think of any two-digit number and reverse it. Add the two numbers. Divide the sum by 11. The quotient will be equal to the sum of the digits of the number that was thought.
Think of any two-digit number and reverse it. Subtract the smaller number from the larger. Divide the answer by 9. The quotient will be equal to the difference in digits of the number which was thought.
Think of a three digit number. Write it by reversing the digits. Find their difference. Now this Difference + 99 = Difference between the hundreds digit and ones digit.
A number is divisible by 10 just when its ones digit is 0.
If we subtract the ones digit of a number from that number, the portion left over is a multiple of 10.
If the ones digit of a number is 0 or 5, then it is divisible by 5.
If the ones digit of a number is even, then the number itself is even.
If the ones digit of a number is odd, then the number itself is odd.
If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.
If the sum of the digits of a number is divisible by 3, then number is divisible by 3.
If a number is divisible by both 2 and 3, it must be divisible by 6.
A number is divisible by 4, if the number formed by tens and units digits is divisible by 4.
A number is divisible by 11, if the difference of the sum of digits at even places and the sum of digits at odd places (beginning from units place) is either 0 or a multiple of 11.
A three-digit number is a multiple of 11, if the sum of its outer two digits minus its middle digit is a multiple of 11.
Graphs represent a wide variety of data in an easy-to-read format for quick and ready comprehension.
Three useful kinds of graphs are
Line graphs are usually used to show changes in amounts or results over a period of time.
Bar graphs are generally used to compare amounts or results. They are used to show categories which are different from each other.
Circle graphs are designed to show relative proportions. The angle of a sector of a circle is made proportional to the percent of an item of the data list to be displayed. They are used to represent data where all categories or groups are specified.
The position of a point on a plane is fixed by specifying its distances from two fixed lines perpendicular to each other.
In an ordered pair the x-coordinate is always stated first. The coordinates are always written in this order and thus they are called ordered pair.