Express each of the following as a rational number in the form pq-i 6-1ii -7-1iii 14-1iv -4-1 -32-1v 35-1 - 52-1

(i) nbsp;6 1=16 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; — gt; (a−1 = 1/a) ( ...

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Byju's Answer

Standard XII

Mathematics

Union

Express each ...

Question

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

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Solution

$(i) 6^{- 1} = \frac{1}{6}$ ---> (a⁻¹ = 1/a)

$(ii) (- 7)^{- 1} = \frac{1}{- 7}$ ---> (a⁻¹ = 1/a)
= $\frac{- 1}{7}$

$(iii) {(\frac{1}{4})}^{- 1} = \frac{1}{1 / 4}$ ---> (a⁻¹ = 1/a)
$= 4$

(iv) $(- 4)^{- 1} \times {(\frac{- 3}{2})}^{- 1} = \frac{1}{- 4} \times \frac{1}{- 3 / 2}$ ---> (a⁻¹ = 1/a)
$= \frac{1}{- 4} \times \frac{2}{- 3}$
$= \frac{1}{6}$

$(v)left(frac{3}{5} right )^{-1}times left(frac{5}{2} right )^{-1}=frac{1}{3/5}times frac{1}{5/2}$ ---> (a⁻¹ = 1/a)
$= \frac{5}{3} \times \frac{2}{5}$
$= \frac{2}{3}$

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Similar questions

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) (4)⁻¹
(ii) (−6)⁻¹
(iii)

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

(iv)

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

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

\frac{p}{q} :

(i)

\frac{- 8}{3} + \frac{- 1}{4} + \frac{- 11}{6} + \frac{3}{8} - 3

(ii)

\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}

(iii)

\frac{15}{2} + \frac{9}{8} + \frac{- 11}{3} + 6 + \frac{- 7}{6}

(iv)

\frac{- 7}{4} + 0 + \frac{- 9}{5} + \frac{19}{10} + \frac{11}{14}

(v)

\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2

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

\frac{p}{q}

:
(i)

{(\frac{3}{7})}^{2}

(ii)

{(\frac{7}{9})}^{3}

(iii)

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

Now can you write the meaning of the expressions below in ordinary language?

(i)

(ii)

(iii)

(iv)

(v) x + y + 2

(vi)

(vii) ab + 1

(viii) (a + 1) (b + 1)

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Express each of the following as a rational number in the form pq: (i) 6−1 (ii) (−7)−1 (iii) 14-1 (iv) (-4)-1×-32-1 (v) 35-1×52-1

(i) 6-1=16 ---> (a−1 = 1/a) (ii) (-7)-1=1-7 ---> (a−1 = 1/a) =-17 (iii) 14-1=11/4 ---> (a−1 = 1/a) =4 (iv) (-4)-1×-32-1=1-4×1-3/2 ---> (a−1 = 1/a) =1-4×2-3 =16 ---> (a−1 = 1/a) =53×25 =23

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