nine times the reciprocal of a rational number is 6 times the reciprocal of 17 .find the rational number.

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Solution

$Let the required rational number = x Now, its reciprocal = \frac{1}{x} Now, according to question : 9 \times \frac{1}{x} = 6 \times \frac{1}{17} \Rightarrow \frac{9}{x} = \frac{6}{17} \Rightarrow x = \frac{17 \times 9}{6} = \frac{51}{2} So, the required rational number = \frac{51}{2}$

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Fill in the blanks :

(i)The product of two positive rational numbers is always_______________.
(iii) The product of two negative rational numbers is always_______________.

(iv) The reciprocal of a positive rational number is _______________.

(v) The reciprocal of a negative rational number is _______________.

(vi) Zero has _______________ reciprocal.

(vii) The product of a rational number and its reciprocal is ____________.

(viii) The numbers_______________and_______________are their own reciprocals.

(ix) If a is reciprocal of b, then the reciprocal of b is _______________.

(x) The number 0 is __________________ the reciprocal of any number.

(xi) Reciprocal of $\frac{1}{a}, a \neq$ is __________________.

(xii) $(17 \times 12)^{- 1} = 17^{- 1} \times$ __________________.

Q. Fill in the blanks:
(i) The product of two positive rational numbers is always .....
(ii) The product of a positive rational number and a negative rational number is always .....
(iii) The product of two negative rational numbers is always .....
(iv) The reciprocal of a positive rational number is .....
(v) The reciprocal of a negative rational number is .....
(vi) Zero has ..... reciprocal.
(vii) The product of a rational number and its reciprocal is .....
(viii) The numbers ..... and ..... are their own reciprocals.
(ix) If a is reciprocal of b, then the reciprocal of b is .....
(x) The number 0 is ..... the reciprocal of any number.
(xi) Reciprocal of

\frac{1}{a}, a \neq 0

is .....
(xii) (17 × 12)⁻¹ = 17⁻¹ × .....

Q. The reciprocal of a negative rational number is

Fill in the blanks :
(i) The product of two positive rational numbers is always___
(ii) The product of two negative rational numbers is always___
(iii) If two rational numbers have opposite signs then their product is always___
(iv) The reciprocal of a positive rational number is ___ and the reciprocal of a negative rational number is___
(v) Rational number 0 has___ reciprocal.
(vi) The product of a rational number and its reciprocal is ___
(vii) The numbers ___and ___are their own reciprocals.
(viii) If M is reciprocal on N,then the reciprocal of N is___

Q. Fill in the blanks:
(i) The product of a rational number and its reciprocal is .......
(ii) Zero has ....... reciprocal.
(iii) The numbers ....... and ....... are their own reciprocals.
(iv) zero is ....... the reciprocal of any number.
(v) The reciprocal of a, where a ≠ 0, is .......
(vi) The reciprocal of

\frac{1}{a}

, where a ≠ 0, is .......
(vii) The reciprocal of a positive rational rational number is .......
(viii) The reciprocal of a negative rational number is .......

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nine times the reciprocal of a rational number is 6 times the reciprocal of 17 .find the rational number.

Let the required rational number = xNow, its reciprocal = 1xNow, according to question : 9×1x = 6×117⇒9x = 617⇒x = 17×96 = 512So, the required rational number = 512

$Let the required rational number = x Now, its reciprocal = \frac{1}{x} Now, according to question : 9 \times \frac{1}{x} = 6 \times \frac{1}{17} \Rightarrow \frac{9}{x} = \frac{6}{17} \Rightarrow x = \frac{17 \times 9}{6} = \frac{51}{2} So, the required rational number = \frac{51}{2}$