rationalnumbers
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Rational Numbers
Name : Nishant RohatgiClass : VIII ARoll No. : 25
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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.
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Examples of Rational Numbers• 16• 1/2 • 8• 1.33
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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.
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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.
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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
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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.
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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.
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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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Thank You