Real Number System Class 8th Mathematics Term 1 Tamilnadu Board Solution

Class 8th Mathematics Term 1 Tamilnadu Board Solution
Exercise 1.1
  1. The additive identity of rational numbers is ________. Choose the correct…
  2. The additive inverse of -3/5 is ______. Choose the correct answer:A. -3/5 B.…
  3. The reciprocal of -5/13 is _______. Choose the correct answer:A. 5/13 B. -13/5…
  4. The multiplicative inverse of -7 is ___________. Choose the correct answer:A. 7…
  5. ________ has no reciprocal. Choose the correct answer:A. 0 B. 1 C. -1 D. 1/4…
  6. (-3/7) + 1/9 = 1/9 + (-3/7) Name the property under addition used in each of…
  7. 4/9 + (7/8 + 1/2) = (4/9 + 7/8) + 1/2 Name the property under addition used in…
  8. 8 + 7/10 = 7/10 + 8 Name the property under addition used in each of the…
  9. (-7/15) + 0 = -7/15 = 0 + (-7/15) Name the property under addition used in each…
  10. 2/5 + (-2/5) = 0 Name the property under addition used in each of the…
  11. 2/3 x 4/5 = 4/5 x 2/3 Name the property under multiplication used in each of…
  12. (-3/4) x 1 = -3/4 = 1 x (-3/4) Name the property under multiplication used in…
  13. (-17/28) x (-28/17) = 1 Name the property under multiplication used in each of…
  14. 1/5 x (7/8 x 4/3) = (1/5 x 7/8) x 4/3 Name the property under multiplication…
  15. 2/7 x (9/10 + 2/5) = 2/7 x 9/10 + 2/7 x 2/5 Name the property under…
  16. 4 and 2/5 Verify whether commutative property is satisfied for addition,…
  17. -3/4 -2/7 Verify whether commutative property is satisfied for addition,…
  18. 1/3 , 2/5 -3/7 Verify whether associative property is satisfied for addition,…
  19. 2/3 , -4/5 9/10 Verify whether associative property is satisfied for addition,…
  20. -5/4 x (8/9 + 5/7) Use distributive property of multiplication of rational…
  21. 2/7 x (1/4 - 1/2) Use distributive property of multiplication of rational…
Exercise 1.2
  1. 4/3 and 2/5 Find one rational number between the following pairs of rational…
  2. -2/7 and 5/6 Find one rational number between the following pairs of rational…
  3. 5/11 and 7/8 Find one rational number between the following pairs of rational…
  4. 7/4 and 8/3 Find one rational number between the following pairs of rational…
  5. 2/7 and 3/5 Find two rational numbers between
  6. 6/5 and 9/11 Find two rational numbers between
  7. 1/3 and 4/5 Find two rational numbers between
  8. -1/6 and 1/3 Find two rational numbers between
  9. 1/4 and 1/2 Find three rational numbers between
  10. 1/10 and 2/3 Find three rational numbers between
  11. -1/3 and 3/2 Find three rational numbers between
  12. 1/8 and 1/12 Find three rational numbers between
Exercise 1.3
  1. 2 x 5/3 = ________ Choose the correct answer:A. 10/3 B. 2 5/6 C. 10/6 D. 2/3…
  2. 2/5 x 4/7 = ________ Choose the correct answer:A. 14/20 B. 8/35 C. 20/14 D.…
  3. 2/5 + 4/9 is _________ Choose the correct answer:A. 10/23 B. 8/45 C. 38/45 D.…
  4. 1/5 / 2 1/2 is _________ Choose the correct answer:A. 2/25 B. 1/2 C. 10/7 D.…
  5. (1 - 1/2) + (3/4 - 1/4) Choose the correct answer:A. 0 B. 1 C. 1/2 D. 3/4…
  6. 11/12 / (5/9 x 18/25) Simplify:
  7. (2 1/2 x 8/10) / (1 1/2 + 5/8) Simplify:
  8. 15/16 (5/6 - 1/2) / 10/11 Simplify:
  9. 9/8 / 3/5 (3/4 + 3/5) Simplify:
  10. 2/5 / 1/5 [3/4 - 1/2]-1 Simplify:
  11. (1 3/4 x 3 1/7) - (4 3/8 / 5 3/5) Simplify:
  12. (1/6 + 2 3/4 1 7/11) / 1 1/6 Simplify:
  13. (- 1/3) - (2/3 x 1/7) Simplify:
Exercise 1.4
  1. am × an is equal to Choose the correct answer for the following:A. am + an B.…
  2. p^0 is equal to Choose the correct answer for the following:A. 0 B. 1 C. -1 D.…
  3. In 10^2 , the exponent is Choose the correct answer for the following:A. 2 B. 1…
  4. 6-1 is equal to Choose the correct answer for the following:A. 6 B. -1 C. - 1/6…
  5. The multiplicative inverse of 2-4 is Choose the correct answer for the…
  6. (-2)-5 × (-2)^6 is equal to Choose the correct answer for the following:A. -2…
  7. (-2)-2 is equal to Choose the correct answer for the following:A. 1/2 B. 1/4 C.…
  8. (2^0 + 4-1) × 2^2 is equal to Choose the correct answer for the following:A. 2…
  9. (1/3)^-4 is equal to Choose the correct answer for the following:A. 3 B. 3^4 C.…
  10. (-1)^50 is equal to Choose the correct answer for the following:A. -1 B. 50 C.…
  11. (-4)^5 ÷ (-4)^8 Simplify:
  12. (1/2^3)^2 Simplify:
  13. (-3)^4 x (5/3)^4 Simplify:
  14. (2/3)^5 x (3/4)^2 x (1/5)^2 Simplify:
  15. (3-7 ÷ 3^10) × 3-5 Simplify:
  16. 2^6 x 3^2 x 2^3 x 3^7/2^8 x 3^6 Simplify:
  17. ya - b × yb - c × yc - a Simplify:
  18. (4p)^3 × (2p)^2 × p^4 Simplify:
  19. Simplify:
  20. (1/4)^-2 - 3 x 8^2/3 x x 4^0 + (9/16)^-1/2 Simplify:
  21. (3^0 + 4-1) × 2^2 Find the value of:
  22. (2-1 × 4-1) ÷ 2-2 Find the value of:
  23. (1/2)^-2 + (1/3)^-2 + (1/4)^-2 Find the value of:
  24. (3-1 + 4-1 + 5-1)^0 Find the value of:
  25. [(-2/3)^-2]^2 Find the value of:
  26. 7-20 - 7-21 Find the value of:
  27. 5m ÷ 5-3 = 5^5 Find the value of m for which
  28. 4m = 64 Find the value of m for which
  29. 8m - 3 = 1 Find the value of m for which
  30. (a^3)m = a^9 Find the value of m for which
  31. (5m)^2 × (25)^3 × 125^2 = 1 Find the value of m for which
  32. 2m = (8)^1/3 / (2^3)^2/3 Find the value of m for which
  33. If 2x = 16, find i. x ii. 2^x/2 iii. 22x iv. 2x + 2 v. root 2^-x
  34. If 3x = 81, find i. x ii. 3x + 3 iii. 3x/2 iv. 32x v. 3x - 6
  35. 3^x+1/3^x (x+1) x (3^x/3)^x+1 = 1 Prove that
  36. Prove that
Exercise 1.5
  1. Just observe the unit digits and state which of the following are not perfect…
  2. 78^2 Write down the unit digits of the following:
  3. 27^2 Write down the unit digits of the following:
  4. 41^2 Write down the unit digits of the following:
  5. 35^2 Write down the unit digits of the following:
  6. 42^2 Write down the unit digits of the following:
  7. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 Find the sum of the following numbers without…
  8. 1 + 3 + 5 + 7 Find the sum of the following numbers without actually adding the…
  9. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 Find the sum of the following numbers…
  10. 7^2 Express the following as a sum of consecutive odd numbers starting with 1…
  11. 9^2 Express the following as a sum of consecutive odd numbers starting with 1…
  12. 5^2 Express the following as a sum of consecutive odd numbers starting with 1…
  13. 11^2 Express the following as a sum of consecutive odd numbers starting with 1…
  14. 3/8 Find the squares of the following numbers
  15. 7/10 Find the squares of the following numbers
  16. 1/5 Find the squares of the following numbers
  17. 2/3 Find the squares of the following numbers
  18. 31/40 Find the squares of the following numbers
  19. (-3)^2 Find the values of the following:
  20. (-7)^2 Find the values of the following:
  21. (-0.3)^2 Find the values of the following:
  22. (- 2/3)^2 Find the values of the following:
  23. (- 3/4)^2 Find the values of the following:
  24. (-0.6)^2 Find the values of the following:
  25. 1^2 + 2^2 + 2^2 = 3^2 , 2^2 + 3^2 + 6^2 = 7^2 3^2 + 4^2 + 12^2 + 13^2 4^2 + 5^2…
  26. 11^2 = 121 101^2 = 10201 1001^2 = 1002001 100001^2 = 10000200001 10000001^2 =…
Exercise 1.6
  1. 3 × 3 × 4 × 4 Find the square root of each expression given below:…
  2. 2 × 2 × 5 × 5 Find the square root of each expression given below:…
  3. 3 × 3 × 3 × 3 × 3 × 3 Find the square root of each expression given below:…
  4. 5 × 5 × 11 × 11 × 7 × 7 Find the square root of each expression given below:…
  5. 9/64 Find the square root of the following:
  6. 1/16 Find the square root of the following:
  7. 49 Find the square root of the following:
  8. 16 Find the square root of the following:
  9. 2304 Find the square root of each of the following by Long division method:…
  10. 4489 Find the square root of each of the following by Long division method:…
  11. 3481 Find the square root of each of the following by Long division method:…
  12. 529 Find the square root of each of the following by Long division method:…
  13. 3249 Find the square root of each of the following by Long division method:…
  14. 1369 Find the square root of each of the following by Long division method:…
  15. 5776 Find the square root of each of the following by Long division method:…
  16. 7921 Find the square root of each of the following by Long division method:…
  17. 576 Find the square root of each of the following by Long division method:…
  18. 3136 Find the square root of each of the following by Long division method:…
  19. 729 Find the square root of the following numbers by the factorization method:…
  20. 400 Find the square root of the following numbers by the factorization method:…
  21. 1764 Find the square root of the following numbers by the factorization method:…
  22. 4096 Find the square root of the following numbers by the factorization method:…
  23. 7744 Find the square root of the following numbers by the factorization method:…
  24. 9604 Find the square root of the following numbers by the factorization method:…
  25. 5929 Find the square root of the following numbers by the factorization method:…
  26. 9216 Find the square root of the following numbers by the factorization method:…
  27. 529 Find the square root of the following numbers by the factorization method:…
  28. 8100 Find the square root of the following numbers by the factorization method:…
  29. 2.56 Find the square root of the following decimal numbers:
  30. 7.29 Find the square root of the following decimal numbers:
  31. 51.84 Find the square root of the following decimal numbers:
  32. 42.25 Find the square root of the following decimal numbers:
  33. 31.36 Find the square root of the following decimal numbers:
  34. 0.2916 Find the square root of the following decimal numbers:
  35. 11.56 Find the square root of the following decimal numbers:
  36. 0.001849 Find the square root of the following decimal numbers:
  37. 402 Find the least number which must be subtracted from each of the following…
  38. 1989 Find the least number which must be subtracted from each of the following…
  39. 3250 Find the least number which must be subtracted from each of the following…
  40. 825 Find the least number which must be subtracted from each of the following…
  41. 4000 Find the least number which must be subtracted from each of the following…
  42. 525 Find the least number which must be added to each of the following numbers…
  43. 1750 Find the least number which must be added to each of the following numbers…
  44. 252 Find the least number which must be added to each of the following numbers…
  45. 1825 Find the least number which must be added to each of the following numbers…
  46. 6412 Find the least number which must be added to each of the following numbers…
  47. 2 Find the square root of the following correct to two places of decimals:…
  48. 5 Find the square root of the following correct to two places of decimals:…
  49. 0.016 Find the square root of the following correct to two places of decimals:…
  50. 7/8 Find the square root of the following correct to two places of decimals:…
  51. 1 1/12 Find the square root of the following correct to two places of decimals:…
  52. Find the length of the side of a square where area is 441 m^2 .
  53. 225/3136 Find the square root of the following:
  54. 2116/3481 Find the square root of the following:
  55. 529/1764 Find the square root of the following:
  56. 7921/5776 Find the square root of the following:
Exercise 1.7
  1. Which of the following numbers is a perfect cube? Choose the correct answer for…
  2. Which of the following numbers is not a perfect cube? Choose the correct answer…
  3. The cube of an odd natural number is Choose the correct answer for the…
  4. The number of zeros of the cube root of 1000 is Choose the correct answer for…
  5. The unit digit of the cube of the number 50 is Choose the correct answer for…
  6. The number of zeros at the end of the cube of 100 is Choose the correct answer…
  7. Find the smallest number by which the number 108 must be multiplied to obtain a…
  8. Find the smallest number by which the number 88 must be divided to obtain a…
  9. The volume of a cube is 64 cm^3 . The side of the cube is Choose the correct…
  10. Which of the following is false? Choose the correct answer for the following:A.…
  11. 400 Check whether the following are perfect cubes?
  12. 216 Check whether the following are perfect cubes?
  13. 729 Check whether the following are perfect cubes?
  14. 250 Check whether the following are perfect cubes?
  15. 1000 Check whether the following are perfect cubes?
  16. 900 Check whether the following are perfect cubes?
  17. 128 Which of the following numbers are not perfect cubes?
  18. 100 Which of the following numbers are not perfect cubes?
  19. 64 Which of the following numbers are not perfect cubes?
  20. 125 Which of the following numbers are not perfect cubes?
  21. 72 Which of the following numbers are not perfect cubes?
  22. 625 Which of the following numbers are not perfect cubes?
  23. 81 Find the smallest number by which each of the following number must be…
  24. 128 Find the smallest number by which each of the following number must be…
  25. 135 Find the smallest number by which each of the following number must be…
  26. 192 Find the smallest number by which each of the following number must be…
  27. 704 Find the smallest number by which each of the following number must be…
  28. 625 Find the smallest number by which each of the following number must be…
  29. 243 Find the smallest number by which each of the following number must be…
  30. 256 Find the smallest number by which each of the following number must be…
  31. 72 Find the smallest number by which each of the following number must be…
  32. 675 Find the smallest number by which each of the following number must be…
  33. 100 Find the smallest number by which each of the following number must be…
  34. 729 Find the cube root of each of the following numbers by prime Factorization…
  35. 343 Find the cube root of each of the following numbers by prime Factorization…
  36. 512 Find the cube root of each of the following numbers by prime Factorization…
  37. 0.064 Find the cube root of each of the following numbers by prime…
  38. 0.216 Find the cube root of each of the following numbers by prime…
  39. 5 23/64 Find the cube root of each of the following numbers by prime…
  40. - 1.331 Find the cube root of each of the following numbers by prime…
  41. - 27000 Find the cube root of each of the following numbers by prime…
  42. The volume of a cubical box is 19.683 cu. cm. Find the length of each side of…
Exercise 1.8
  1. 12.568 Express the following correct to two decimal places:
  2. 25.416 kg Express the following correct to two decimal places:
  3. 39.927 m Express the following correct to two decimal places:
  4. 56.596 m Express the following correct to two decimal places:
  5. 41.056 m Express the following correct to two decimal places:
  6. 729.943 km Express the following correct to two decimal places:
  7. 0.0518 m Express the following correct to three decimal places:
  8. 3.5327 km Express the following correct to three decimal places:
  9. 58.2936l Express the following correct to three decimal places:
  10. 0.1327 gm Express the following correct to three decimal places:
  11. 365.3006 Express the following correct to three decimal places:
  12. 100.1234 Express the following correct to three decimal places:
  13. 247 to the nearest ten. Write the approximate value of the following numbers to…
  14. 152 to the nearest ten. Write the approximate value of the following numbers to…
  15. 6848 to the nearest hundred. Write the approximate value of the following…
  16. 14276 to the nearest ten thousand. Write the approximate value of the following…
  17. 3576274 to the nearest Lakhs. Write the approximate value of the following…
  18. 104, 3567809 to the nearest crore Write the approximate value of the following…
  19. 22.266 Round off the following numbers to the nearest integer:
  20. 777.43 Round off the following numbers to the nearest integer:
  21. 402.06 Round off the following numbers to the nearest integer:
  22. 305.85 Round off the following numbers to the nearest integer:
  23. 299.77 Round off the following numbers to the nearest integer:
  24. 9999.9567 Round off the following numbers to the nearest integer:…
Exercise 1.9
  1. 40, 35, 30, ___, ___, ___. Complete the following patterns:
  2. 0, 2, 4, ___, ___, ___. Complete the following patterns:
  3. 84, 77, 70, ___, ___, ___. Complete the following patterns:
  4. 4.4, 5.5, 6.6, ___, ___, ___. Complete the following patterns:
  5. 1, 3, 6, 10, ___, ___, ___. Complete the following patterns:
  6. 1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___ (This sequence is called FIBONACCI…
  7. 1, 8, 27, 64, ___, ___, ___. Complete the following patterns:
  8. A water tank has steps inside it. A monkey is sitting on the top most step. (ie,…
  9. A vendor arranged his apples as in the following pattern: A. If there are ten…

Exercise 1.1
Question 1.

Choose the correct answer:

The additive identity of rational numbers is ________.
A. 0

B. 1

C. -1

D. 2


Answer:

Let, additive identity of rational number is = x


Let, a rational number is = p/q, where q ≠ 0


According to problem,


⇒ p/q + x = p/q


⇒ x = 0


∴ The additive identity of rational number is = 0


Question 2.

Choose the correct answer:

The additive inverse of  is ______.
A. 

B. 

C. 

D. 


Answer:

Let, additive inverse of -3/5 is = x


According to problem,


⇒ -3/5 + x = 0


⇒ x = 3/5


∴ The additive inverse of -3/5 is = 3/5


Question 3.

Choose the correct answer:

The reciprocal of  is _______.
A. 

B. 

C. 

D. 


Answer:

Let, reciprocal of  is = x


According to problem,




∴ The reciprocal of 


Question 4.

Choose the correct answer:

The multiplicative inverse of -7 is ___________.
A. 7

B. 1/7

C. -7

D. -1/7


Answer:

Let, multiplicative inverse of -7 is = x


According to problem,


⇒ (-7) × x = 1


⇒ x = -1/7


∴ The multiplicative inverse of -7 is = -1/7


Question 5.

Choose the correct answer:

________ has no reciprocal.
A. 0

B. 1

C. -1

D. 


Answer:

Among the following numbers 0 has no reciprocal.


∵ reciprocal of 0 = 1/0, which is not possible.


∴ Denominator of a fraction cannot be equal to 0.


Question 6.

Name the property under addition used in each of the following:



Answer:

It is under Commutative property of addition.


Where change in the positions of the operands does not change the result.




Question 7.

Name the property under addition used in each of the following:



Answer:

It is under Associative property of addition.


Where change in the grouping of numbers does not change the result.




Question 8.

Name the property under addition used in each of the following:



Answer:

It is under Commutative property of addition.


Where change in the positions of the operands does not change the result.




Question 9.

Name the property under addition used in each of the following:



Answer:

It is under the property Additive identity.


The sum of 0 and any rational number is the rational number itself.




Question 10.

Name the property under addition used in each of the following:



Answer:

It is under the property additive inverse.


Where addition of two rational numbers is 0.




Question 11.

Name the property under multiplication used in each of the following:



Answer:

It is under Commutative property of multiplication.


Where change in the positions of the operands does not change the result.




Question 12.

Name the property under multiplication used in each of the following:



Answer:

It is under the property multiplicative identity.


The product of any rational number and 1 is the rational number itself.




Question 13.

Name the property under multiplication used in each of the following:



Answer:

It is under the property Multiplicative inverse.


When multiplication of two rational number is = 1.




Question 14.

Name the property under multiplication used in each of the following:



Answer:

It is under Associative property of multiplication.


Where change in the grouping of numbers does not change the result.




Question 15.

Name the property under multiplication used in each of the following:



Answer:

It is under the Distributive property of multiplication over addition.


Where ⇒ a × (b + c) = a × b + a × c




Question 16.

Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.

4 and 


Answer:

A. Commutative property for addition:


We have to prove,


⇒ 4 + 2/5 = 2/5 + 4


LHS,





RHS,





∴ LHS= RHS


∴ Commutative property for addition is satisfied.


B. Commutative property for subtraction:


We have to prove,


⇒ 4 – 2/5 = 2/5 – 4


LHS,





RHS,





∴ LHS ≠ RHS


∴ Commutative property for subtraction is not satisfied.


C. Commutative property for multiplication:


We have to prove,


⇒ 4 × 2/5 = 2/5 × 4


LHS,




RHS,




∴ LHS= RHS


∴ Commutative property for multiplication is satisfied.


D. Commutative property for division:


We have to prove that,



LHS,




⇒ 10


RHS,





∴ LHS ≠ RHS


∴ Commutative property for division is not satisfied.



Question 17.

Verify whether commutative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.



Answer:

A. Commutative property for addition:


We have to prove,



LHS,





RHS,





∴ LHS= RHS


∴ Commutative property for addition is satisfied.


B. Commutative property for subtraction:


We have to prove,



LHS,






RHS,






∴ LHS ≠ RHS


∴ Commutative property for subtraction is not satisfied.


C. Commutative property for multiplication:


We have to prove,



LHS,




RHS,




∴ LHS= RHS


∴ Commutative property for multiplication is satisfied.


D. Commutative property for division:


We have to prove that,



LHS,




⇒ 21/8


RHS,





∴ LHS ≠ RHS


∴ Commutative property for division is not satisfied.



Question 18.

Verify whether associative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.



Answer:

A. Associative property for addition:


We have to prove that,



LHS,







RHS,







∴ LHS = RHS


∴ Associative property for addition is satisfied.


B. Associative property for Subtraction:


We have to prove that,



LHS,







RHS,







∴ LHS ≠ RHS


∴ Associative property for Subtraction is not satisfied.


C. Associative property for multiplication:


We have to prove that,



LHS,





RHS,





∴ LHS= RHS


∴ Associative property for multiplication is satisfied.


D. Associative Property for division:


We have to prove that,



LHS,







RHS,







∴ LHS ≠ RHS


∴ Associative property for Division is not satisfied.



Question 19.

Verify whether associative property is satisfied for addition, subtraction, multiplication and division of the following pairs of rational numbers.



Answer:

A. Associative property for addition:


We have to prove that,



LHS,







RHS,







∴ LHS = RHS


∴ Associative property for addition is satisfied.


B. Associative property for Subtraction:


We have to prove that,



LHS,







RHS,








∴ LHS ≠ RHS


∴ Associative property for Subtraction is not satisfied.


C. Associative property for multiplication:


We have to prove that,



LHS,





RHS,





∴ LHS= RHS


∴ Associative property for multiplication is satisfied.


D. Associative Property for division:


We have to prove that,



LHS,







RHS,







∴ LHS ≠ RHS


∴ Associative property for Divission is not satisfied.



Question 20.

Use distributive property of multiplication of rational numbers and simplify:



Answer:

According to distributive property of multiplication of rational numbers,









Question 21.

Use distributive property of multiplication of rational numbers and simplify:



Answer:

According to distributive property of multiplication of rational numbers,









Exercise 1.2
Question 1.

Find one rational number between the following pairs of rational numbers.

 and 


Answer:

Let, q is the rational number between 4/3 and 2/5.






∴ one rational number between 4/3 and 2/5 is = 13/15



Question 2.

Find one rational number between the following pairs of rational numbers.

 and 


Answer:

Let, q is the rational number between -2/7 and 5/6






∴ one rational number between -2/7 and 5/6 is = 23/84



Question 3.

Find one rational number between the following pairs of rational numbers.

 and 


Answer:

Let, q is the rational number between 5/11 and 7/8






∴ one rational number between 5/11 and 7/8 is = 117/176



Question 4.

Find one rational number between the following pairs of rational numbers.

 and 


Answer:

Let, q is the rational number between 7/4 and 8/3






∴ one rational number between 7/4 and 8/3 is = 53/24



Question 5.

Find two rational numbers between

 and 


Answer:

Let, p and q are two rational numbers between 2/7 and 3/5




⇒ p = 31/70




⇒ q = 51/140


∴ Two rational numbers between 2/7 and 3/5 is = 31/70 and 51/140



Question 6.

Find two rational numbers between

 and 


Answer:

Let, p and q are two rational numbers between 6/5 and 9/11








∴ Two rational numbers between 6/5 and 9/11 is = 111/110 and 243/220



Question 7.

Find two rational numbers between

 and 


Answer:

Let, p and q are two rational numbers between 1/3 and 4/5










∴ Two rational numbers between 1/3 amd 4/5 is = 17/30 and 9/20



Question 8.

Find two rational numbers between

 and 


Answer:

Let, p and q are two rational numbers between -1/6 and 1/3










∴ Two rational numbers between -1/6 and 1/3 is = 1/12 and -1/24



Question 9.

Find three rational numbers between

 and 


Answer:

Let, p, q and r are three rational numbers between 1/4 and 1/2














∴ Three rational numbers between 1/4 and 1/2 is = 3/8, 5/16 and 9/32


Question 10.

Find three rational numbers between

 and 


Answer:

Let, p, q and r are three rational numbers between 1/10 and 2/3














∴ Three rational numbers between 1/10 and 2/3 is = 23/60, 29/120, 41/240



Question 11.

Find three rational numbers between

 and 


Answer:

Let, p, q and r are three rational numbers between -1/3 and 3/2














∴ Three rational numbers between -1/3 and 3/2 is = 7/12, 1/8 and -5/48



Question 12.

Find three rational numbers between

 and 


Answer:

Let, p, q and r are three rational numbers between 1/8 and 1/12














∴ Three rational numbers between 1/8 and 1/12 is = 5/48, 11/96 and 23/192




Exercise 1.3
Question 1.

Choose the correct answer:

 = ________
A. 

B. 

C. 

D. 


Answer:





(B) doesn’t match the solution.


(C) doesn’t match the solution.


(D) doesn’t match the solution.


Question 2.

Choose the correct answer:

 = ________
A. 

B. 

C. 

D. 


Answer:




(A) doesn’t match the solution.


(C) doesn’t match the solution.


(D) doesn’t match the solution.


Question 3.

Choose the correct answer:

 is _________
A. 

B. 

C. 

D. 


Answer:





(A) doesn’t match the solution.


(B) doesn’t match the solution.


(D) doesn’t match the solution.


Question 4.

Choose the correct answer:

 is _________
A. 

B. 

C. 

D. 


Answer:










(B) doesn’t match the solution.


(C) doesn’t match the solution.


(D) doesn’t match the solution.


Question 5.

Choose the correct answer:


A. 0

B. 1

C. 

D. 


Answer:



where LCM is least common multiple)





, where LCM is least common multiple)





(A) doesn’t match the solution.


(C) doesn’t match the solution.


(D) doesn’t match the solution.


Question 6.

Simplify:



Answer:
















Question 7.

Simplify:



Answer:

















Question 8.

Simplify:



Answer:



where LCM is least common multiple













Question 9.

Simplify:



Answer:
















Question 10.

Simplify:



Answer: