STD VIII – NUMBER SYSTEM (Online)
About Course
RATIONAL NUMBERS
Numbers that can be expressed in the form pq, where p and q are integers and q ≠ 0, are known as rational numbers. The collection of rational numbers is denoted by Q.
A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are integers
Properties of rational Numbers
Closure
Commutativity (a+b=b+a) and (a x b = b x a) |
Associativity a×(b×c)=(a×b)×c and a+(b+c)=(a+b)+c
Number Line
Every point in a number line, represents a number
Between any 2 rational numbers there exists infinitely many rational numbers
Exponents
Very large numbers, for example, 1685742300000 are difficult to read, understand and compare.
Exponents are shorthand for repeated multiplication of the same thing by itself, and it’s power refers to the number of times it is multiplied.
Squares and Square Roots.
In mathematics, students learn about numbers and different operations on them.
A square of an integer is the product of some integer with itself. Similarly, the square root of a number is an integer which when multiplied by itself give this number. In this topic, we will increase our understanding of squares, square roots, and will learn about ways of finding them.
Cubes and Cube Roots.
In arithmetic and algebra, the cube of a number n is its third power, the result of the number multiplied by itself twice:
n3 = n × n × n.
It is also the number multiplied by its square:
n3 = n × n2.
Playing with Numbers.
Calculations with numbers are done with arithmetical operations, the most familiar being the addition, subtraction, multiplication, division, and exponentiation.
Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers.
Sets.
In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}
Course Content
RATIONAL NUMBERS
What are Rational Numbers
Operations Performed on Rational numbers
Addition
Subtraction
Multiplication
Division
Numerical Word problems
Representation in Decimal
Rational numbers as extension of integers
Decimal representation of
rational numbers
Problem solving using
operations on rational
numbers and decimal
fractions
Fraction as an operator
Reciprocal of a fraction
Multiplication and
division of decimal
fractions
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QUIZ – RATIONAL NUMBERS
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03:41
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QUIZ – DECIMAL REPRESENTATION OF RATIONAL NUMBERS
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QUIZ – PROPERTIES OF RATIONAL NUMBERS
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04:38
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QUIZ – IRRATIONAL NUMBERS
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04:33
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03:23
EXPONENTS
Exponents only natural
numbers.
Laws of exponents
(through observing
patterns to arrive at
generalisation.)
Application of laws of
exponents in simple daily
life problems
SQUARES AND SQUARE ROOTS
Square and Square roots
using factor method and
division method for
numbers containing (a)
no more than total 4 digits
and (b) no more than 2
decimal places
Division Method to find square roots
CUBES AND CUBES ROOT
Find Cubes and Cube roots of numbers
Only factor Method for numbers containing more than three digits
PLAYING WITH NUMBERS
Writing and
understanding a 2 and 3
digit number in
generalized form (100a +
10b + c , where a, b, c can
be only digit 0-9) and
engaging with various
puzzles Children to solve
and create problems and
puzzles.
Deducing the divisibility
test rules of 2, 3, 5, 9, 10
for a two or three-digit
number expressed in the
general form
SETS
Union and intersection of
sets
Disjoint set
Complement of a set
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