NOW ENROLLING FOR TEST SERIES I.C.S.E. 2023 -24 STD VIII IX AND X

STD VIII – NUMBER SYSTEM (Online)

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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}

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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

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

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