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Rational numbers class 8
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- 2. Rational numbers arenumbers in the form of 𝑝 𝑞 where, 𝑞 ≠ 0. For e.g.: 3 4 , −9 8 , −3 5 , 6 4 RATIONAL NUMBERS
- 3. DIFFERENCE BETWEEN FRACTION& RATIONAL NUMBER Rational Numbers Fractions RATIONAL NUMBERS = POSITIVE FRACTIONS + NEGETIVE FRACTIONS
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- 5. PROPERTIES OF RATIONALNUMBERS
- 6. CLOSURE PROPERTY Closureproperty means that if we divide/ add/ subtract/ multiply a rational number the answer should always be a rational number if one of the case becomes wrong then the whole law is wrong.
- 7. 2 3 + 4 5 = 10 + 12 15 = 22 15 Addition Sinceby adding two rational numbers answer is also rational number . therefore , addition of rational numbers is closed.
- 8. 2 3 − 4 5 = 10 − 12 15 = −2 15 Subtraction Sinceby subtracting two rational numbers answer is also rational number. Therefore, subtraction of rational number is closed.
- 9. 2 4 × −8 9 = −4 9 Multiplication Since by multiplyingtwo rational numbers answer is also rational number. Therefore, multiplication of rational number is closed.
- 10. 2 5 ÷ 3 10 = 2 5 × 10 3 = 4 3 7 1 ÷ 0 7 = 7 1 × 7 0 = 𝑛 ⋅𝑑 Division of rational number is not closed.
- 11. COMMUTATIVE PROPERTY Commutativeproperty means, that by interchanging the position of rational numbers the answer should be same. 𝑝 𝑤 + 𝑞 𝑛 = 𝑞 𝑛 + 𝑝 𝑤
- 12. 1 2 + 6 2 = 7 2 6 2 + 1 2 − 7 2 Addition Since by interchangingthe position of rational numbers the answer is same. Therefore, addition of rational numbers is commutative.
- 13. −4 9 − 4 9 = −4 9 − 4 9 = −8 9 4 9 − −4 9 = 4 9 + 4 9 = 8 9 Subtraction Since, by interchangingthe position of rational numbers the answer is not same. Therefore, subtraction of rational numbers is not commutative.
- 14. 2 4 × 3 −8 = 3 −16 3 −8 × 2 4 = 3 −16 Multiplication Since by interchangingthe position of rational numbers the answer is same. Therefore, multiplication of rational numbers is commutative.
- 15. −2 9 ÷ 3 −11 = −2 9 × −11 3 = 22 27 3 −11 ÷ −2 9 = 3 −11 𝑥 9 −2 = 27 22 Division Since by interchangingthe position of rational numbers the answer is not same. Therefore, division of rational numbers is not commutative.
- 16. ASSOCIATIVE PROPERTY Associativeproperty means that by interchanging the position of three rational numbers the answer should be same. 𝑝 𝑞 + 𝑛 𝑚 + 𝑥 𝑦 = 𝑥 𝑦 + 𝑛 𝑚 + 𝑝 𝑞
- 17. 9 2 + 6 2 + 1 2 = 9 2 + 7 2 = 16 2 1 2 + 6 2 + 9 2 = 15 2 + 1 2 = 16 2 Addition Since by interchangingthe position of rational numbers the answer is same. Therefore, addition of rational numbers is associative.
- 18. −𝟏 𝟑 − 4 3 − 𝟐 𝟑 = −𝟏 𝟑 − 𝟐 𝟑 = −𝟑 𝟑 2 3 − 4 3 − −1 3 = 𝟐 𝟑 − 4 3 + 1 3 = 2 3 − 5 3 = −3 3 Subtraction Since by interchangingthe position of rational numbers the answer is same. Therefore, subtraction of rational numbers is associative.
- 19. 2 4 × 4 9 × 12 4 = 2 4 × 4 3 = 2 3 12 4 × 4 9 × 2 4 = 12 4 × 2 9 = 4 6 = 2 3 Multiplication Since by interchangingthe position of rational numbers the answer is same. Therefore, multiplication of rational numbers is associative.
- 20. 1 4 ÷ 6 9 ÷ 3 1 = 1 4 ÷ 6 9 × 1 3 = 1 4 ÷ 3 9 = 1 4 × 9 3 = 3 4 3 1 ÷ 6 9 ÷ 1 4 = 3 1 ÷ 6 9 × 4 1 = 3 1 ÷ 8 3 = 3 1 × 3 8 = 9 8 Division Since by interchangingthe position of rational numbers the answer is not same. Therefore, division of rational numbers is not associative.
- 21. DISTRIBUTIVE PROPERTY Thisproperty is only of multiplication and is taken over by addition or subtraction.
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- 24. MULTIPLICATIVE IDENTITY • Multiplicativeidentity means that if we will multiply any number by a number the answer will always be same. • 1 is the multiplicative identity for rational numbers. As it will not change the identity of rational number or any integer. • For example: a. 1 2 × 1 = 1 2 b. 5 6 × 1 = 5 6
- 25. ADDITIVE IDENTITY • Additiveidentity means that if we add any number by a number the answer will always be same. • Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well. • For example: a. 0 + −9 = −9 b. 0 + 9 2 = 9 2
- 26. RECIPROCAL OF RATIONAL NUMBERS •Reciprocal of rational numbers means upside down. • NUMBER -2 RECIPROCAL –½
- 27. MULTIPLICATIVE INVERSE • Upsidedown • Number -4 Multiplicative inverse = -¼ • Number -0 Multiplicative = 1/0 = n.d ( does not exist )
- 28. ADDITIVE INVERSE • Oppositein sign • Number =3 additive inverse = (-3 ) • Number = -5 additive inverse = 5
- 29. REPRESENTATION OF RATIONAL NUMBERSON NUMBER LINE 0 -1 -2 -4 -3 -5 5 4 3 2 1
- 32. HOW TO FINDRATIONAL NUMVERS BETWEEN NUMBER LINE? •Take out the equivalent fraction of the rational numbers and write the rational numbers lying between them.
- 33. a. −3 &− 4 − 36 12 & − 48 12 −37/12 , −38/12 , −39 /12 , −40/12 , −41 TO FIND RATIONAL NOS. IN BETWEEN RATIONAL NUMBERS.
- 34. 3 4 & 4 5 15 20 & 16 20 150 200 & 160 200 151/200 , 152/200, 153 /200 , 154 /200 , 155/200 , 156/200 , 157 /200
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- 36. Q1. Is 0 7 a rationalnumber? YES NO
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- 38. Additive identity of56 is:
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- 40. Reciprocal of 6/7is: -7/6 7/6 -6/7 6/-7
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- 42. Which of thefollowing is the Multiplicative identity for rational numbers? 1 None of these 0 -1
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- 44. Which of thefollowing lies between 0 and -1? 0 4/3 -2/3 -3
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- 46. Which of thefollowing is additive inverse of 7/29? 29/7 7/29 -7/29 -29/7
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- 48. Which of thefollowing is multiplicative inverse of 15/31? 31/15 15/31 -15/31 -31/15
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- 50. Which of theproperties indicate give operation: a + b + c = c + b + a Associative Property Closure Property Commutative property Distributive property
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