Rational Numbers

Name : Nishant RohatgiClass : VIII ARoll No. : 25

Rational Numbers A rational number is a real number that can

be written as a ratio of two integers. A rational number written in decimal form is

or repeating.

Examples of Rational Numbers• 16• 1/2 • 8• 1.33

What are integers?• Integers are the whole numbers and their negatives• Examples of integers are

6-120186-934

Integers are rational numbers because they can be written as fraction with 1 as the denominator.

PROPERTIES OF ADDITION OF RATIONAL NUMBERS1) CLOSURE PROPERTY:

The sum of two rational no. is always a rational number. for eg: if a/b and c/d are any 2 rational numbers then a/b+c/d is also a rational number

2) Commutative property: If , a and b are two integers , then , a+ b =b + a

3) Associative property: If a , b and c are any three integers then a+(b + c)=(a + b)+c.

1) Re-arrangement property: The sum of three or more rational numbers remains the same , whatever may be the order of their addition.

Property of zero: If we add zero to any integer , its value does not change. If x is any integer then , x+ 0=0+x.

PROPERTIES OF SUBSTRACTION OF RATIONAL NUMBERS

1. The difference of two rational numbers is a rational number . For exmple if a/ b and c/d are any two rational numbers a/b-c/d is a rational number

2. If a/b is a rational number , then a/b – 0 = a/b

PROPERTIES OF MULTIPLICATION OF RATIONAL NUMBERS

1. Commutative property: If x and y are two integers , then x * y = y * x

2. Associative property: If x , y , z are any three integers, then x*(y*z)=(x*y)*z

3. Distributive property of multiplication over addition : If x , y , z are any three integers, then x* ( y + z ) = x * y + x * z and x* ( y - z ) = x * y - x * z

1. Multiplication by 1 : The value of rational number remains unchanged by multiplying it by 1. for ex -4/7 * 1 = -4/7

1. Multiplication by 0 : If we multiply fraction by zero or vice-versa , the product is zero. For ex -4/7*0= 0.

RECIPROCAL OF A RATIONAL NUMBER

1. A rational number b/a is called a reciprocal or multiplicative inverse of a rational number a/b. a/b * b/a = b/a * a/b = 1.

2. 1 and -1 are the only rational numbers which are their own reciprocals.

PROPERTIES OF DIVISION OF RATIONAL NUMBERS

1. If p/q and q/r are any two rational numbers and q/r ≠ 0 , then p/q ÷ q/r is always a rational number.

2. For any rational number p/q , p/q÷1 =p/q ; p/q÷(-1) = -p/q

3. For every non rational number p/q p/q ÷ p/q = 1 ; p/q ÷ {-p/q} = -1 ; {-p/q} ÷ { p/q } = -1

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