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Rational Numbers

The integers which are in the form of p/q where q u2260 0 are known as Rational Numbers.<br>

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Rational Numbers

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  1. RATIONAL NUMBERS Created By Kajal

  2. Definitionof RationalNumbers Theintegers which are in theformofp/q where q ≠ 0areknown as Rational Numbers. Examples: 5/8;-3/14;7/-15;-6/-11

  3. Propertiesof RationalNumbers 1)ClosureProperty 2)AssociativeProperty 3)DistributiveLaw 4)AdditiveInverse 5)MultiplicativeInverse

  4. Closure Property Rational numbers are closedunder addition.That is,for any two rational numbers a and b, a+b salso a rational number For Example - 8 + 3 = 11 ( a rationalnumber.) Rational numbers are closedunder multiplication.That is,for any two rational numbers a and b,a * b isalso a rationalnumber. For Example - 4 * 2 = 8 (a rational number.)

  5. CommutativeProperty Addition Rational numbers can beaddedinanyorder. Therefore,additionis commutativefor rational numbers. For Example :- -3/8+ 1/7 (-21 +8)/56=(8 – 21)/56 -13/56=-13/56 =1/7+(-3/8)

  6. Subtraction Subtraction isnot commutativefor rationalnumbers For Example - Since, -7 is unequal to7 Hence, L.H.S. Isunequal toR.H.S - 3/7 – 1/7 ≠ 3/7– (- 1/7 )

  7. Multiplication Rational numbers can bemultiplied inanyorder. Therefore,it issaidthat multiplicationiscommutativefor rationalnumbers. ForExample:-7/3*6/5 = 6/5* (-7/3) -14/5 -14/5 =

  8. AssociativeProperty Addition Addition isassociative for rational numbers.Thatisfor any threerational numbers a, band c, : a + (b+ c) = (a + b)+ c. ForExample: 2+ (5+3) 2+8 =(2 +5) +3 = = 7 +3 10 10

  9. Multiplication Multiplication isassociative for rational numbers.That isfor any rational numbers a, band c : a* (b*c) = (a*b) * c For Example : 2* (5*3) 2*15 = = = (2*5)*3 10*3 30 30

  10. DistributiveLaw For all rational numbersa, b and c, a (b+c) = ab+ ac a (b-c) = ab– ac 2(5-3)= 2*5- 2*3 10-6 4 2(5+3)= 2*5 +2*3 10+6 16 ForExample: 2*2 4 = = 2*8 16 = =

  11. AdditiveInverse Additive inverseisalsoknown as negativeof a number.For anyrational number a/b, a/b+(-a/b)= (-a/b)+a/b = 0 Therefore,‘-a/b’is theadditiveinverseof‘a/b’and ‘a/b’istheAdditive Inverseof(-a/b).

  12. Multiplicative Inverse Multiplicative inverseisalso known as reciprocalnumber.For any rational number a/b, a/b* b/a = 1

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