##### Class 8^{th} Mathematics Term 1 Tamilnadu Board Solution

**Exercise 1.1**- The additive identity of rational numbers is ________. Choose the correct…
- The additive inverse of -3/5 is ______. Choose the correct answer:A. -3/5 B.…
- The reciprocal of -5/13 is _______. Choose the correct answer:A. 5/13 B. -13/5…
- The multiplicative inverse of -7 is ___________. Choose the correct answer:A. 7…
- ________ has no reciprocal. Choose the correct answer:A. 0 B. 1 C. -1 D. 1/4…
- (-3/7) + 1/9 = 1/9 + (-3/7) Name the property under addition used in each of…
- 4/9 + (7/8 + 1/2) = (4/9 + 7/8) + 1/2 Name the property under addition used in…
- 8 + 7/10 = 7/10 + 8 Name the property under addition used in each of the…
- (-7/15) + 0 = -7/15 = 0 + (-7/15) Name the property under addition used in each…
- 2/5 + (-2/5) = 0 Name the property under addition used in each of the…
- 2/3 x 4/5 = 4/5 x 2/3 Name the property under multiplication used in each of…
- (-3/4) x 1 = -3/4 = 1 x (-3/4) Name the property under multiplication used in…
- (-17/28) x (-28/17) = 1 Name the property under multiplication used in each of…
- 1/5 x (7/8 x 4/3) = (1/5 x 7/8) x 4/3 Name the property under multiplication…
- 2/7 x (9/10 + 2/5) = 2/7 x 9/10 + 2/7 x 2/5 Name the property under…
- 4 and 2/5 Verify whether commutative property is satisfied for addition,…
- -3/4 -2/7 Verify whether commutative property is satisfied for addition,…
- 1/3 , 2/5 -3/7 Verify whether associative property is satisfied for addition,…
- 2/3 , -4/5 9/10 Verify whether associative property is satisfied for addition,…
- -5/4 x (8/9 + 5/7) Use distributive property of multiplication of rational…
- 2/7 x (1/4 - 1/2) Use distributive property of multiplication of rational…

**Exercise 1.2**- 4/3 and 2/5 Find one rational number between the following pairs of rational…
- -2/7 and 5/6 Find one rational number between the following pairs of rational…
- 5/11 and 7/8 Find one rational number between the following pairs of rational…
- 7/4 and 8/3 Find one rational number between the following pairs of rational…
- 2/7 and 3/5 Find two rational numbers between
- 6/5 and 9/11 Find two rational numbers between
- 1/3 and 4/5 Find two rational numbers between
- -1/6 and 1/3 Find two rational numbers between
- 1/4 and 1/2 Find three rational numbers between
- 1/10 and 2/3 Find three rational numbers between
- -1/3 and 3/2 Find three rational numbers between
- 1/8 and 1/12 Find three rational numbers between

**Exercise 1.3**- 2 x 5/3 = ________ Choose the correct answer:A. 10/3 B. 2 5/6 C. 10/6 D. 2/3…
- 2/5 x 4/7 = ________ Choose the correct answer:A. 14/20 B. 8/35 C. 20/14 D.…
- 2/5 + 4/9 is _________ Choose the correct answer:A. 10/23 B. 8/45 C. 38/45 D.…
- 1/5 / 2 1/2 is _________ Choose the correct answer:A. 2/25 B. 1/2 C. 10/7 D.…
- (1 - 1/2) + (3/4 - 1/4) Choose the correct answer:A. 0 B. 1 C. 1/2 D. 3/4…
- 11/12 / (5/9 x 18/25) Simplify:
- (2 1/2 x 8/10) / (1 1/2 + 5/8) Simplify:
- 15/16 (5/6 - 1/2) / 10/11 Simplify:
- 9/8 / 3/5 (3/4 + 3/5) Simplify:
- 2/5 / 1/5 [3/4 - 1/2]-1 Simplify:
- (1 3/4 x 3 1/7) - (4 3/8 / 5 3/5) Simplify:
- (1/6 + 2 3/4 1 7/11) / 1 1/6 Simplify:
- (- 1/3) - (2/3 x 1/7) Simplify:

**Exercise 1.4**- am × an is equal to Choose the correct answer for the following:A. am + an B.…
- p^0 is equal to Choose the correct answer for the following:A. 0 B. 1 C. -1 D.…
- In 10^2 , the exponent is Choose the correct answer for the following:A. 2 B. 1…
- 6-1 is equal to Choose the correct answer for the following:A. 6 B. -1 C. - 1/6…
- The multiplicative inverse of 2-4 is Choose the correct answer for the…
- (-2)-5 × (-2)^6 is equal to Choose the correct answer for the following:A. -2…
- (-2)-2 is equal to Choose the correct answer for the following:A. 1/2 B. 1/4 C.…
- (2^0 + 4-1) × 2^2 is equal to Choose the correct answer for the following:A. 2…
- (1/3)^-4 is equal to Choose the correct answer for the following:A. 3 B. 3^4 C.…
- (-1)^50 is equal to Choose the correct answer for the following:A. -1 B. 50 C.…
- (-4)^5 ÷ (-4)^8 Simplify:
- (1/2^3)^2 Simplify:
- (-3)^4 x (5/3)^4 Simplify:
- (2/3)^5 x (3/4)^2 x (1/5)^2 Simplify:
- (3-7 ÷ 3^10) × 3-5 Simplify:
- 2^6 x 3^2 x 2^3 x 3^7/2^8 x 3^6 Simplify:
- ya - b × yb - c × yc - a Simplify:
- (4p)^3 × (2p)^2 × p^4 Simplify:
- Simplify:
- (1/4)^-2 - 3 x 8^2/3 x x 4^0 + (9/16)^-1/2 Simplify:
- (3^0 + 4-1) × 2^2 Find the value of:
- (2-1 × 4-1) ÷ 2-2 Find the value of:
- (1/2)^-2 + (1/3)^-2 + (1/4)^-2 Find the value of:
- (3-1 + 4-1 + 5-1)^0 Find the value of:
- [(-2/3)^-2]^2 Find the value of:
- 7-20 - 7-21 Find the value of:
- 5m ÷ 5-3 = 5^5 Find the value of m for which
- 4m = 64 Find the value of m for which
- 8m - 3 = 1 Find the value of m for which
- (a^3)m = a^9 Find the value of m for which
- (5m)^2 × (25)^3 × 125^2 = 1 Find the value of m for which
- 2m = (8)^1/3 / (2^3)^2/3 Find the value of m for which
- If 2x = 16, find i. x ii. 2^x/2 iii. 22x iv. 2x + 2 v. root 2^-x
- If 3x = 81, find i. x ii. 3x + 3 iii. 3x/2 iv. 32x v. 3x - 6
- 3^x+1/3^x (x+1) x (3^x/3)^x+1 = 1 Prove that
- Prove that

**Exercise 1.5**- Just observe the unit digits and state which of the following are not perfect…
- 78^2 Write down the unit digits of the following:
- 27^2 Write down the unit digits of the following:
- 41^2 Write down the unit digits of the following:
- 35^2 Write down the unit digits of the following:
- 42^2 Write down the unit digits of the following:
- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 Find the sum of the following numbers without…
- 1 + 3 + 5 + 7 Find the sum of the following numbers without actually adding the…
- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 Find the sum of the following numbers…
- 7^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 9^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 5^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 11^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 3/8 Find the squares of the following numbers
- 7/10 Find the squares of the following numbers
- 1/5 Find the squares of the following numbers
- 2/3 Find the squares of the following numbers
- 31/40 Find the squares of the following numbers
- (-3)^2 Find the values of the following:
- (-7)^2 Find the values of the following:
- (-0.3)^2 Find the values of the following:
- (- 2/3)^2 Find the values of the following:
- (- 3/4)^2 Find the values of the following:
- (-0.6)^2 Find the values of the following:
- 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…
- 11^2 = 121 101^2 = 10201 1001^2 = 1002001 100001^2 = 10000200001 10000001^2 =…

**Exercise 1.6**- 3 × 3 × 4 × 4 Find the square root of each expression given below:…
- 2 × 2 × 5 × 5 Find the square root of each expression given below:…
- 3 × 3 × 3 × 3 × 3 × 3 Find the square root of each expression given below:…
- 5 × 5 × 11 × 11 × 7 × 7 Find the square root of each expression given below:…
- 9/64 Find the square root of the following:
- 1/16 Find the square root of the following:
- 49 Find the square root of the following:
- 16 Find the square root of the following:
- 2304 Find the square root of each of the following by Long division method:…
- 4489 Find the square root of each of the following by Long division method:…
- 3481 Find the square root of each of the following by Long division method:…
- 529 Find the square root of each of the following by Long division method:…
- 3249 Find the square root of each of the following by Long division method:…
- 1369 Find the square root of each of the following by Long division method:…
- 5776 Find the square root of each of the following by Long division method:…
- 7921 Find the square root of each of the following by Long division method:…
- 576 Find the square root of each of the following by Long division method:…
- 3136 Find the square root of each of the following by Long division method:…
- 729 Find the square root of the following numbers by the factorization method:…
- 400 Find the square root of the following numbers by the factorization method:…
- 1764 Find the square root of the following numbers by the factorization method:…
- 4096 Find the square root of the following numbers by the factorization method:…
- 7744 Find the square root of the following numbers by the factorization method:…
- 9604 Find the square root of the following numbers by the factorization method:…
- 5929 Find the square root of the following numbers by the factorization method:…
- 9216 Find the square root of the following numbers by the factorization method:…
- 529 Find the square root of the following numbers by the factorization method:…
- 8100 Find the square root of the following numbers by the factorization method:…
- 2.56 Find the square root of the following decimal numbers:
- 7.29 Find the square root of the following decimal numbers:
- 51.84 Find the square root of the following decimal numbers:
- 42.25 Find the square root of the following decimal numbers:
- 31.36 Find the square root of the following decimal numbers:
- 0.2916 Find the square root of the following decimal numbers:
- 11.56 Find the square root of the following decimal numbers:
- 0.001849 Find the square root of the following decimal numbers:
- 402 Find the least number which must be subtracted from each of the following…
- 1989 Find the least number which must be subtracted from each of the following…
- 3250 Find the least number which must be subtracted from each of the following…
- 825 Find the least number which must be subtracted from each of the following…
- 4000 Find the least number which must be subtracted from each of the following…
- 525 Find the least number which must be added to each of the following numbers…
- 1750 Find the least number which must be added to each of the following numbers…
- 252 Find the least number which must be added to each of the following numbers…
- 1825 Find the least number which must be added to each of the following numbers…
- 6412 Find the least number which must be added to each of the following numbers…
- 2 Find the square root of the following correct to two places of decimals:…
- 5 Find the square root of the following correct to two places of decimals:…
- 0.016 Find the square root of the following correct to two places of decimals:…
- 7/8 Find the square root of the following correct to two places of decimals:…
- 1 1/12 Find the square root of the following correct to two places of decimals:…
- Find the length of the side of a square where area is 441 m^2 .
- 225/3136 Find the square root of the following:
- 2116/3481 Find the square root of the following:
- 529/1764 Find the square root of the following:
- 7921/5776 Find the square root of the following:

**Exercise 1.7**- Which of the following numbers is a perfect cube? Choose the correct answer for…
- Which of the following numbers is not a perfect cube? Choose the correct answer…
- The cube of an odd natural number is Choose the correct answer for the…
- The number of zeros of the cube root of 1000 is Choose the correct answer for…
- The unit digit of the cube of the number 50 is Choose the correct answer for…
- The number of zeros at the end of the cube of 100 is Choose the correct answer…
- Find the smallest number by which the number 108 must be multiplied to obtain a…
- Find the smallest number by which the number 88 must be divided to obtain a…
- The volume of a cube is 64 cm^3 . The side of the cube is Choose the correct…
- Which of the following is false? Choose the correct answer for the following:A.…
- 400 Check whether the following are perfect cubes?
- 216 Check whether the following are perfect cubes?
- 729 Check whether the following are perfect cubes?
- 250 Check whether the following are perfect cubes?
- 1000 Check whether the following are perfect cubes?
- 900 Check whether the following are perfect cubes?
- 128 Which of the following numbers are not perfect cubes?
- 100 Which of the following numbers are not perfect cubes?
- 64 Which of the following numbers are not perfect cubes?
- 125 Which of the following numbers are not perfect cubes?
- 72 Which of the following numbers are not perfect cubes?
- 625 Which of the following numbers are not perfect cubes?
- 81 Find the smallest number by which each of the following number must be…
- 128 Find the smallest number by which each of the following number must be…
- 135 Find the smallest number by which each of the following number must be…
- 192 Find the smallest number by which each of the following number must be…
- 704 Find the smallest number by which each of the following number must be…
- 625 Find the smallest number by which each of the following number must be…
- 243 Find the smallest number by which each of the following number must be…
- 256 Find the smallest number by which each of the following number must be…
- 72 Find the smallest number by which each of the following number must be…
- 675 Find the smallest number by which each of the following number must be…
- 100 Find the smallest number by which each of the following number must be…
- 729 Find the cube root of each of the following numbers by prime Factorization…
- 343 Find the cube root of each of the following numbers by prime Factorization…
- 512 Find the cube root of each of the following numbers by prime Factorization…
- 0.064 Find the cube root of each of the following numbers by prime…
- 0.216 Find the cube root of each of the following numbers by prime…
- 5 23/64 Find the cube root of each of the following numbers by prime…
- - 1.331 Find the cube root of each of the following numbers by prime…
- - 27000 Find the cube root of each of the following numbers by prime…
- The volume of a cubical box is 19.683 cu. cm. Find the length of each side of…

**Exercise 1.8**- 12.568 Express the following correct to two decimal places:
- 25.416 kg Express the following correct to two decimal places:
- 39.927 m Express the following correct to two decimal places:
- 56.596 m Express the following correct to two decimal places:
- 41.056 m Express the following correct to two decimal places:
- 729.943 km Express the following correct to two decimal places:
- 0.0518 m Express the following correct to three decimal places:
- 3.5327 km Express the following correct to three decimal places:
- 58.2936l Express the following correct to three decimal places:
- 0.1327 gm Express the following correct to three decimal places:
- 365.3006 Express the following correct to three decimal places:
- 100.1234 Express the following correct to three decimal places:
- 247 to the nearest ten. Write the approximate value of the following numbers to…
- 152 to the nearest ten. Write the approximate value of the following numbers to…
- 6848 to the nearest hundred. Write the approximate value of the following…
- 14276 to the nearest ten thousand. Write the approximate value of the following…
- 3576274 to the nearest Lakhs. Write the approximate value of the following…
- 104, 3567809 to the nearest crore Write the approximate value of the following…
- 22.266 Round off the following numbers to the nearest integer:
- 777.43 Round off the following numbers to the nearest integer:
- 402.06 Round off the following numbers to the nearest integer:
- 305.85 Round off the following numbers to the nearest integer:
- 299.77 Round off the following numbers to the nearest integer:
- 9999.9567 Round off the following numbers to the nearest integer:…

**Exercise 1.9**- 40, 35, 30, ___, ___, ___. Complete the following patterns:
- 0, 2, 4, ___, ___, ___. Complete the following patterns:
- 84, 77, 70, ___, ___, ___. Complete the following patterns:
- 4.4, 5.5, 6.6, ___, ___, ___. Complete the following patterns:
- 1, 3, 6, 10, ___, ___, ___. Complete the following patterns:
- 1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___ (This sequence is called FIBONACCI…
- 1, 8, 27, 64, ___, ___, ___. Complete the following patterns:
- A water tank has steps inside it. A monkey is sitting on the top most step. (ie,…
- A vendor arranged his apples as in the following pattern: A. If there are ten…

**Exercise 1.1**

- The additive identity of rational numbers is ________. Choose the correct…
- The additive inverse of -3/5 is ______. Choose the correct answer:A. -3/5 B.…
- The reciprocal of -5/13 is _______. Choose the correct answer:A. 5/13 B. -13/5…
- The multiplicative inverse of -7 is ___________. Choose the correct answer:A. 7…
- ________ has no reciprocal. Choose the correct answer:A. 0 B. 1 C. -1 D. 1/4…
- (-3/7) + 1/9 = 1/9 + (-3/7) Name the property under addition used in each of…
- 4/9 + (7/8 + 1/2) = (4/9 + 7/8) + 1/2 Name the property under addition used in…
- 8 + 7/10 = 7/10 + 8 Name the property under addition used in each of the…
- (-7/15) + 0 = -7/15 = 0 + (-7/15) Name the property under addition used in each…
- 2/5 + (-2/5) = 0 Name the property under addition used in each of the…
- 2/3 x 4/5 = 4/5 x 2/3 Name the property under multiplication used in each of…
- (-3/4) x 1 = -3/4 = 1 x (-3/4) Name the property under multiplication used in…
- (-17/28) x (-28/17) = 1 Name the property under multiplication used in each of…
- 1/5 x (7/8 x 4/3) = (1/5 x 7/8) x 4/3 Name the property under multiplication…
- 2/7 x (9/10 + 2/5) = 2/7 x 9/10 + 2/7 x 2/5 Name the property under…
- 4 and 2/5 Verify whether commutative property is satisfied for addition,…
- -3/4 -2/7 Verify whether commutative property is satisfied for addition,…
- 1/3 , 2/5 -3/7 Verify whether associative property is satisfied for addition,…
- 2/3 , -4/5 9/10 Verify whether associative property is satisfied for addition,…
- -5/4 x (8/9 + 5/7) Use distributive property of multiplication of rational…
- 2/7 x (1/4 - 1/2) Use distributive property of multiplication of rational…

**Exercise 1.2**

- 4/3 and 2/5 Find one rational number between the following pairs of rational…
- -2/7 and 5/6 Find one rational number between the following pairs of rational…
- 5/11 and 7/8 Find one rational number between the following pairs of rational…
- 7/4 and 8/3 Find one rational number between the following pairs of rational…
- 2/7 and 3/5 Find two rational numbers between
- 6/5 and 9/11 Find two rational numbers between
- 1/3 and 4/5 Find two rational numbers between
- -1/6 and 1/3 Find two rational numbers between
- 1/4 and 1/2 Find three rational numbers between
- 1/10 and 2/3 Find three rational numbers between
- -1/3 and 3/2 Find three rational numbers between
- 1/8 and 1/12 Find three rational numbers between

**Exercise 1.3**

- 2 x 5/3 = ________ Choose the correct answer:A. 10/3 B. 2 5/6 C. 10/6 D. 2/3…
- 2/5 x 4/7 = ________ Choose the correct answer:A. 14/20 B. 8/35 C. 20/14 D.…
- 2/5 + 4/9 is _________ Choose the correct answer:A. 10/23 B. 8/45 C. 38/45 D.…
- 1/5 / 2 1/2 is _________ Choose the correct answer:A. 2/25 B. 1/2 C. 10/7 D.…
- (1 - 1/2) + (3/4 - 1/4) Choose the correct answer:A. 0 B. 1 C. 1/2 D. 3/4…
- 11/12 / (5/9 x 18/25) Simplify:
- (2 1/2 x 8/10) / (1 1/2 + 5/8) Simplify:
- 15/16 (5/6 - 1/2) / 10/11 Simplify:
- 9/8 / 3/5 (3/4 + 3/5) Simplify:
- 2/5 / 1/5 [3/4 - 1/2]-1 Simplify:
- (1 3/4 x 3 1/7) - (4 3/8 / 5 3/5) Simplify:
- (1/6 + 2 3/4 1 7/11) / 1 1/6 Simplify:
- (- 1/3) - (2/3 x 1/7) Simplify:

**Exercise 1.4**

- am × an is equal to Choose the correct answer for the following:A. am + an B.…
- p^0 is equal to Choose the correct answer for the following:A. 0 B. 1 C. -1 D.…
- In 10^2 , the exponent is Choose the correct answer for the following:A. 2 B. 1…
- 6-1 is equal to Choose the correct answer for the following:A. 6 B. -1 C. - 1/6…
- The multiplicative inverse of 2-4 is Choose the correct answer for the…
- (-2)-5 × (-2)^6 is equal to Choose the correct answer for the following:A. -2…
- (-2)-2 is equal to Choose the correct answer for the following:A. 1/2 B. 1/4 C.…
- (2^0 + 4-1) × 2^2 is equal to Choose the correct answer for the following:A. 2…
- (1/3)^-4 is equal to Choose the correct answer for the following:A. 3 B. 3^4 C.…
- (-1)^50 is equal to Choose the correct answer for the following:A. -1 B. 50 C.…
- (-4)^5 ÷ (-4)^8 Simplify:
- (1/2^3)^2 Simplify:
- (-3)^4 x (5/3)^4 Simplify:
- (2/3)^5 x (3/4)^2 x (1/5)^2 Simplify:
- (3-7 ÷ 3^10) × 3-5 Simplify:
- 2^6 x 3^2 x 2^3 x 3^7/2^8 x 3^6 Simplify:
- ya - b × yb - c × yc - a Simplify:
- (4p)^3 × (2p)^2 × p^4 Simplify:
- Simplify:
- (1/4)^-2 - 3 x 8^2/3 x x 4^0 + (9/16)^-1/2 Simplify:
- (3^0 + 4-1) × 2^2 Find the value of:
- (2-1 × 4-1) ÷ 2-2 Find the value of:
- (1/2)^-2 + (1/3)^-2 + (1/4)^-2 Find the value of:
- (3-1 + 4-1 + 5-1)^0 Find the value of:
- [(-2/3)^-2]^2 Find the value of:
- 7-20 - 7-21 Find the value of:
- 5m ÷ 5-3 = 5^5 Find the value of m for which
- 4m = 64 Find the value of m for which
- 8m - 3 = 1 Find the value of m for which
- (a^3)m = a^9 Find the value of m for which
- (5m)^2 × (25)^3 × 125^2 = 1 Find the value of m for which
- 2m = (8)^1/3 / (2^3)^2/3 Find the value of m for which
- If 2x = 16, find i. x ii. 2^x/2 iii. 22x iv. 2x + 2 v. root 2^-x
- If 3x = 81, find i. x ii. 3x + 3 iii. 3x/2 iv. 32x v. 3x - 6
- 3^x+1/3^x (x+1) x (3^x/3)^x+1 = 1 Prove that
- Prove that

**Exercise 1.5**

- Just observe the unit digits and state which of the following are not perfect…
- 78^2 Write down the unit digits of the following:
- 27^2 Write down the unit digits of the following:
- 41^2 Write down the unit digits of the following:
- 35^2 Write down the unit digits of the following:
- 42^2 Write down the unit digits of the following:
- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 Find the sum of the following numbers without…
- 1 + 3 + 5 + 7 Find the sum of the following numbers without actually adding the…
- 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 Find the sum of the following numbers…
- 7^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 9^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 5^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 11^2 Express the following as a sum of consecutive odd numbers starting with 1…
- 3/8 Find the squares of the following numbers
- 7/10 Find the squares of the following numbers
- 1/5 Find the squares of the following numbers
- 2/3 Find the squares of the following numbers
- 31/40 Find the squares of the following numbers
- (-3)^2 Find the values of the following:
- (-7)^2 Find the values of the following:
- (-0.3)^2 Find the values of the following:
- (- 2/3)^2 Find the values of the following:
- (- 3/4)^2 Find the values of the following:
- (-0.6)^2 Find the values of the following:
- 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…
- 11^2 = 121 101^2 = 10201 1001^2 = 1002001 100001^2 = 10000200001 10000001^2 =…

**Exercise 1.6**

- 3 × 3 × 4 × 4 Find the square root of each expression given below:…
- 2 × 2 × 5 × 5 Find the square root of each expression given below:…
- 3 × 3 × 3 × 3 × 3 × 3 Find the square root of each expression given below:…
- 5 × 5 × 11 × 11 × 7 × 7 Find the square root of each expression given below:…
- 9/64 Find the square root of the following:
- 1/16 Find the square root of the following:
- 49 Find the square root of the following:
- 16 Find the square root of the following:
- 2304 Find the square root of each of the following by Long division method:…
- 4489 Find the square root of each of the following by Long division method:…
- 3481 Find the square root of each of the following by Long division method:…
- 529 Find the square root of each of the following by Long division method:…
- 3249 Find the square root of each of the following by Long division method:…
- 1369 Find the square root of each of the following by Long division method:…
- 5776 Find the square root of each of the following by Long division method:…
- 7921 Find the square root of each of the following by Long division method:…
- 576 Find the square root of each of the following by Long division method:…
- 3136 Find the square root of each of the following by Long division method:…
- 729 Find the square root of the following numbers by the factorization method:…
- 400 Find the square root of the following numbers by the factorization method:…
- 1764 Find the square root of the following numbers by the factorization method:…
- 4096 Find the square root of the following numbers by the factorization method:…
- 7744 Find the square root of the following numbers by the factorization method:…
- 9604 Find the square root of the following numbers by the factorization method:…
- 5929 Find the square root of the following numbers by the factorization method:…
- 9216 Find the square root of the following numbers by the factorization method:…
- 529 Find the square root of the following numbers by the factorization method:…
- 8100 Find the square root of the following numbers by the factorization method:…
- 2.56 Find the square root of the following decimal numbers:
- 7.29 Find the square root of the following decimal numbers:
- 51.84 Find the square root of the following decimal numbers:
- 42.25 Find the square root of the following decimal numbers:
- 31.36 Find the square root of the following decimal numbers:
- 0.2916 Find the square root of the following decimal numbers:
- 11.56 Find the square root of the following decimal numbers:
- 0.001849 Find the square root of the following decimal numbers:
- 402 Find the least number which must be subtracted from each of the following…
- 1989 Find the least number which must be subtracted from each of the following…
- 3250 Find the least number which must be subtracted from each of the following…
- 825 Find the least number which must be subtracted from each of the following…
- 4000 Find the least number which must be subtracted from each of the following…
- 525 Find the least number which must be added to each of the following numbers…
- 1750 Find the least number which must be added to each of the following numbers…
- 252 Find the least number which must be added to each of the following numbers…
- 1825 Find the least number which must be added to each of the following numbers…
- 6412 Find the least number which must be added to each of the following numbers…
- 2 Find the square root of the following correct to two places of decimals:…
- 5 Find the square root of the following correct to two places of decimals:…
- 0.016 Find the square root of the following correct to two places of decimals:…
- 7/8 Find the square root of the following correct to two places of decimals:…
- 1 1/12 Find the square root of the following correct to two places of decimals:…
- Find the length of the side of a square where area is 441 m^2 .
- 225/3136 Find the square root of the following:
- 2116/3481 Find the square root of the following:
- 529/1764 Find the square root of the following:
- 7921/5776 Find the square root of the following:

**Exercise 1.7**

- Which of the following numbers is a perfect cube? Choose the correct answer for…
- Which of the following numbers is not a perfect cube? Choose the correct answer…
- The cube of an odd natural number is Choose the correct answer for the…
- The number of zeros of the cube root of 1000 is Choose the correct answer for…
- The unit digit of the cube of the number 50 is Choose the correct answer for…
- The number of zeros at the end of the cube of 100 is Choose the correct answer…
- Find the smallest number by which the number 108 must be multiplied to obtain a…
- Find the smallest number by which the number 88 must be divided to obtain a…
- The volume of a cube is 64 cm^3 . The side of the cube is Choose the correct…
- Which of the following is false? Choose the correct answer for the following:A.…
- 400 Check whether the following are perfect cubes?
- 216 Check whether the following are perfect cubes?
- 729 Check whether the following are perfect cubes?
- 250 Check whether the following are perfect cubes?
- 1000 Check whether the following are perfect cubes?
- 900 Check whether the following are perfect cubes?
- 128 Which of the following numbers are not perfect cubes?
- 100 Which of the following numbers are not perfect cubes?
- 64 Which of the following numbers are not perfect cubes?
- 125 Which of the following numbers are not perfect cubes?
- 72 Which of the following numbers are not perfect cubes?
- 625 Which of the following numbers are not perfect cubes?
- 81 Find the smallest number by which each of the following number must be…
- 128 Find the smallest number by which each of the following number must be…
- 135 Find the smallest number by which each of the following number must be…
- 192 Find the smallest number by which each of the following number must be…
- 704 Find the smallest number by which each of the following number must be…
- 625 Find the smallest number by which each of the following number must be…
- 243 Find the smallest number by which each of the following number must be…
- 256 Find the smallest number by which each of the following number must be…
- 72 Find the smallest number by which each of the following number must be…
- 675 Find the smallest number by which each of the following number must be…
- 100 Find the smallest number by which each of the following number must be…
- 729 Find the cube root of each of the following numbers by prime Factorization…
- 343 Find the cube root of each of the following numbers by prime Factorization…
- 512 Find the cube root of each of the following numbers by prime Factorization…
- 0.064 Find the cube root of each of the following numbers by prime…
- 0.216 Find the cube root of each of the following numbers by prime…
- 5 23/64 Find the cube root of each of the following numbers by prime…
- - 1.331 Find the cube root of each of the following numbers by prime…
- - 27000 Find the cube root of each of the following numbers by prime…
- The volume of a cubical box is 19.683 cu. cm. Find the length of each side of…

**Exercise 1.8**

- 12.568 Express the following correct to two decimal places:
- 25.416 kg Express the following correct to two decimal places:
- 39.927 m Express the following correct to two decimal places:
- 56.596 m Express the following correct to two decimal places:
- 41.056 m Express the following correct to two decimal places:
- 729.943 km Express the following correct to two decimal places:
- 0.0518 m Express the following correct to three decimal places:
- 3.5327 km Express the following correct to three decimal places:
- 58.2936l Express the following correct to three decimal places:
- 0.1327 gm Express the following correct to three decimal places:
- 365.3006 Express the following correct to three decimal places:
- 100.1234 Express the following correct to three decimal places:
- 247 to the nearest ten. Write the approximate value of the following numbers to…
- 152 to the nearest ten. Write the approximate value of the following numbers to…
- 6848 to the nearest hundred. Write the approximate value of the following…
- 14276 to the nearest ten thousand. Write the approximate value of the following…
- 3576274 to the nearest Lakhs. Write the approximate value of the following…
- 104, 3567809 to the nearest crore Write the approximate value of the following…
- 22.266 Round off the following numbers to the nearest integer:
- 777.43 Round off the following numbers to the nearest integer:
- 402.06 Round off the following numbers to the nearest integer:
- 305.85 Round off the following numbers to the nearest integer:
- 299.77 Round off the following numbers to the nearest integer:
- 9999.9567 Round off the following numbers to the nearest integer:…

**Exercise 1.9**

- 40, 35, 30, ___, ___, ___. Complete the following patterns:
- 0, 2, 4, ___, ___, ___. Complete the following patterns:
- 84, 77, 70, ___, ___, ___. Complete the following patterns:
- 4.4, 5.5, 6.6, ___, ___, ___. Complete the following patterns:
- 1, 3, 6, 10, ___, ___, ___. Complete the following patterns:
- 1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___ (This sequence is called FIBONACCI…
- 1, 8, 27, 64, ___, ___, ___. Complete the following patterns:
- A water tank has steps inside it. A monkey is sitting on the top most step. (ie,…
- 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,

**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

**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:**

**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:**