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Multiply : (i) (3)/(4)by (5)/(7) (ii)...

Multiply :
(i) `(3)/(4)`by `(5)/(7)`
(ii) `(9)/(8)` by `(32)/(2)`
(iii)(7)/(6)` by 24
`(iv) (-2)/(3)` by `(6)/(7)`
(v) ` (-12)/(5)` by (10)/(-3)`
(vi) `(25)/(-9)` by `(3)/(-10)`
(vii) `(-7)/(10)` by `(-40)/(21)`
(viii) `(-36)/(5)` by `(20)/(-3)`
(ix) `(-13)/(15)` by `(-25)/(26)`

Text Solution

AI Generated Solution

The correct Answer is:
Let's solve the multiplication of the given rational numbers step by step. ### Step-by-Step Solution: **(i)** Multiply \( \frac{3}{4} \) by \( \frac{5}{7} \): \[ \frac{3}{4} \times \frac{5}{7} = \frac{3 \times 5}{4 \times 7} = \frac{15}{28} \] **(ii)** Multiply \( \frac{9}{8} \) by \( \frac{32}{2} \): \[ \frac{9}{8} \times \frac{32}{2} = \frac{9 \times 32}{8 \times 2} = \frac{288}{16} = 18 \] **(iii)** Multiply \( \frac{7}{6} \) by \( 24 \): \[ \frac{7}{6} \times 24 = \frac{7 \times 24}{6} = \frac{168}{6} = 28 \] **(iv)** Multiply \( \frac{-2}{3} \) by \( \frac{6}{7} \): \[ \frac{-2}{3} \times \frac{6}{7} = \frac{-2 \times 6}{3 \times 7} = \frac{-12}{21} = \frac{-4}{7} \] **(v)** Multiply \( \frac{-12}{5} \) by \( \frac{10}{-3} \): \[ \frac{-12}{5} \times \frac{10}{-3} = \frac{-12 \times 10}{5 \times -3} = \frac{120}{15} = 8 \] **(vi)** Multiply \( \frac{25}{-9} \) by \( \frac{3}{-10} \): \[ \frac{25}{-9} \times \frac{3}{-10} = \frac{25 \times 3}{-9 \times -10} = \frac{75}{90} = \frac{5}{6} \] **(vii)** Multiply \( \frac{-7}{10} \) by \( \frac{-40}{21} \): \[ \frac{-7}{10} \times \frac{-40}{21} = \frac{-7 \times -40}{10 \times 21} = \frac{280}{210} = \frac{4}{3} \] **(viii)** Multiply \( \frac{-36}{5} \) by \( \frac{20}{-3} \): \[ \frac{-36}{5} \times \frac{20}{-3} = \frac{-36 \times 20}{5 \times -3} = \frac{720}{15} = 48 \] **(ix)** Multiply \( \frac{-13}{15} \) by \( \frac{-25}{26} \): \[ \frac{-13}{15} \times \frac{-25}{26} = \frac{-13 \times -25}{15 \times 26} = \frac{325}{390} = \frac{65}{78} = \frac{5}{6} \] ### Summary of Results: 1. \( \frac{15}{28} \) 2. \( 18 \) 3. \( 28 \) 4. \( \frac{-4}{7} \) 5. \( 8 \) 6. \( \frac{5}{6} \) 7. \( \frac{4}{3} \) 8. \( 48 \) 9. \( \frac{5}{6} \)
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Multiply :(3)/(4)by(5)/(7) (ii) (3)/(7)by((-4)/(5))((-5)/(9)) by 4( iv) ((-36)/(7))by(-(28)/(9))

Find each of the following products: {:((i)(3)/(5)xx(-7)/(5),(ii)(-9)/(2) xx (5)/(4),(iii)(-6)/(11) xx (-5)/(3)),((iv) (-2)/(3) xx (6)/(7),(v)(-12)/(5)xx(10)/(-3),(vi) (25)/(-9)xx(3)/(-10)), ((vii) (5)/(-18)xx(-9)/(20),(viii) (-13)/(15) xx (-25)/(26), (ix) (16)/(-21)xx(14)/(5)), ((x) (-7)/(6) xx 24,(x i) (7)/(24)xx (-48), (x ii) (-13)/(5)xx(-10)):}

Add the following rational numbers : (i) (12)/(7) and (3)/(7) : (ii) (-2)/(5) and (1)/(5) (iii) (3)/(8) and (1)/(8) (iv) (-5)/(11) and (7)/(-11) (v) (9)/(-13) and (-11)/(-13) (vi) (-2)/(9) and (5)/(9) (vii) -(17)/(9) and (-11)/(9) (viii) (-3)/(7) and (5)/(-7)

Subtract : (i) (3)/(4) from (1)/(3) (ii) (-5)/(6) from (1)/(3) (iii) (-8)/(9) from (-3)/(5) (iv) (-9)/(7) from -1 (v) (-18)/(11)from1 (vi) (-13)/(9) from0 (vii) (32)/(13) from (-6)/(5) (viii) -7 from (-4)/(7) (ix) (5)/(9) from (-2)/(3) (x) 5 from (-3)/(5)

Evaluate : (i) (3)/(4)-(4)/(5) (ii) -3-(4)/(7) (iii) (7)/(24)-(19)/(36) (iv) (14)/(15)-(13)/(20) (v) (4)/(9)-(2)/(-3) (vi) (7)/(11)- (-4)/(-11) (vii) (-5)/(14) -(-2)/(7) (viii) (-5)/(-8)-(-3)/(4)

Subtract: (i) (3)/(4) from (1)/(3) (ii) (-5)/(6) from (1)/(3) (iii) (-8)/(9) from (-3)/(5) (iv) (-9)/(7) from -1 (v) (-18)/(11) from 1 (vi) (-13)/(9) from 0 (vii) (-32)/(13) form (-6)/(5) (viii) -7 from (-4)/(7)

Add the following rational numbers: (i) (3)/(4) and (-3)/(5) (ii) (5)/(8) and (-7)/(12) ,(iii) (-8)/(9) and (11)/(6) ,((iv) (-5)/(16) and (7)/(24) ,(v) (7)/(-18) and (8)/(27) ,(vi) (1)/(-12) and (2)/(-15) , (vii) -1 and (3)/(4) ,(viii) 2 and (-5)/(4) ,(ix) 0 and (-2)/(5)

Simplify : (i) (3)/(20)xx(4)/(5) (ii) (-7)/(30)xx(5)/(14) (iii) (5)/(-18)xx(-9)/(20) (iv) (-9)/(8)xx(-16)/(3) (v) -32xx(-7)/(36) (vi) (16)/(-21)xx(-14)/(5)

Verify the following: (i) (-12)/(5)+(2)/(7)=(2)/(7)+(-12)/(5) (ii) (-5)/(8)+(-9)/(13)= (-9)/(13)+(-5)/(8) (iii) 3+(-7)/(12)=(-7)/(12)+3 (iv) (2)/(-7)+(12)/(-35)=(12)/(-35)+(2)/(-7)