Express each of the following as a rational number-i 4-1ii -6-1iii 13-1iv -23-1

(i) 4 1=41 1=141=14 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nb ...

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Standard VII

Mathematics

Introduction: Rational Numbers

Express each ...

Question

Express each of the following as a rational number:

(i) (4)⁻¹
(ii) (−6)⁻¹
(iii) ${(\frac{1}{3})}^{- 1}$
(iv) ${(\frac{- 2}{3})}^{- 1}$

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Solution

(i) ${(4)}^{- 1} = {(\frac{4}{1})}^{- 1} = {(\frac{1}{4})}^{1} = \frac{1}{4}$ [since ${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$ ]

(ii) ${(- 6)}^{- 1} = {(\frac{- 6}{1})}^{- 1} = {(\frac{1}{- 6})}^{1} = \frac{- 1}{6}$ [since ${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$ ]

(iii) ${(\frac{1}{3})}^{- 1} = {(\frac{3}{1})}^{1} = \frac{3}{1}$ [since ${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$ ]

(iv) ${(\frac{- 2}{3})}^{- 1} = {(\frac{3}{- 2})}^{1} = \frac{- 3}{2}$ [since ${(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}$ ]

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Similar questions

Q. Express each of the following as a rational number in the form

\frac{p}{q} :

(i) 6⁻¹
(ii) (−7)⁻¹
(iii)

{(\frac{1}{4})}^{- 1}

(iv)

(- 4)^{- 1} \times {(\frac{- 3}{2})}^{- 1}

(v)

{(\frac{3}{5})}^{- 1} \times {(\frac{5}{2})}^{- 1}

Express each of the following as a rational number in the form $\frac{p}{q} :$

$(i) 6^{- 1} (i i) (- 7)^{- 1} (i i i) {(\frac{1}{4})}^{- 1} (i v) (- 4)^{- 1} \times {(\frac{- 3}{2})}^{- 1} (v) {(\frac{3}{5})}^{- 1} \times {(\frac{5}{2})}^{- 1}$

Q. Express each of the following as a rational number:

(i)

{(\frac{2}{3})}^{5}

(ii)

{(\frac{- 8}{5})}^{3}

(iii)

{(\frac{- 13}{11})}^{2}

(iv)

{(\frac{1}{6})}^{3}

(v)

{(\frac{- 1}{2})}^{5}

(vi)

{(\frac{- 3}{2})}^{4}

(vii)

{(\frac{- 4}{7})}^{3}

(viii) (−1)_⁹

Q. Simplify each of the following and express each as a rational number:

(i)

{(\frac{3}{2})}^{4} \times {(\frac{1}{5})}^{2}

(ii)

{(\frac{- 2}{3})}^{5} \times {(\frac{- 3}{7})}^{3}

(iii)

{(\frac{- 1}{2})}^{5} \times 2^{3} \times {(\frac{3}{5})}^{2}

(iv)

{(\frac{2}{3})}^{2} \times {(\frac{- 3}{5})}^{3} \times {(\frac{7}{2})}^{2}

(v)

\{{(\frac{- 3}{4})}^{3} - {(\frac{- 5}{2})}^{3}\} \times 4^{2}

Express each of the following rational numbers as a sum of an integer and rational number:

i) -22/5

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Express each of the following as a rational number: (i) (4)−1 (ii) (−6)−1 (iii) 13-1 (iv) -23-1

(i) 4-1=41-1=141=14 [since ab-n=ban] (ii) -6-1=-61-1=1-61=-16 [since ab-n=ban] (iii) 13-1=311=31 [since ab-n=ban] (iv) -23-1=3-21=-32 [since ab-n=ban]

Express each of the following as a rational number:

(i) (4)⁻¹
(ii) (−6)⁻¹
(iii) ${(\frac{1}{3})}^{- 1}$
(iv) ${(\frac{- 2}{3})}^{- 1}$