Find the multiplicative inverse (reciprocal) of each of the following rational numbers:
(i) 9
(ii) -7
(iii) \( \dfrac{12}{5}\)
(iv) \(\dfrac{ -7}{9}\)
(v) \( \dfrac{-3}{-5}\)
(vi) \(\dfrac{ 2}{3} × \dfrac{9}{4}\)
(vii) \( \dfrac{-5}{8} × \dfrac{16}{15}\)
(viii) -2 × \( \dfrac{-3}{5}\)
(ix) -1
(x) \( \dfrac{0}{3}\)
(xi) 1
(i) The reciprocal of 9 is \( \dfrac{ 1}{9}\)
(ii) The reciprocal of -7 is \(\dfrac{ -1}{7}\)
(iii) The reciprocal of \( \dfrac{ 12}{5}\) is \( \dfrac{5}{12}\)
(iv) The reciprocal of \( \dfrac{ -7}{9}\) is \( \dfrac{ 9}{-7}\)
(v) The reciprocal of \( \dfrac{ -3}{-5}\)is \( \dfrac{ 5}{3}\)
(vi) The reciprocal of \( \dfrac{ 2}{3}\) × \( \dfrac{ 9}{4}\) is
Firstly solve for \( \dfrac{ 2}{3}× \dfrac{ 0}{4}= \dfrac{ 1}{1}× \dfrac{ 3}{2} = \dfrac{ 3}{2}\)
The reciprocal of \( \dfrac{ 3}{2}\) is \( \dfrac{ 2}{3}\)
(vii) The reciprocal of \(\dfrac{ -5}{8} × \dfrac{16}{15}\)
Firstly solve for \( \dfrac{ -5}{8} × \dfrac{16}{15}=\dfrac{ -1}{1} × \dfrac{ 2}{3} = \dfrac{ -2}{3}\)
The reciprocal of \( \dfrac{- 2}{3}\) is \( \dfrac{ 3}{-2}\)
(viii) The reciprocal of \( -2 × \dfrac{-3}{5}\)
Firstly solve for \( -2 × \dfrac{-3}{5}=\dfrac{6}{5}\)
The reciprocal of \( \dfrac{6}{5}\)is \( \dfrac{5}{6}\)
(ix) The reciprocal of -1 is -1
(x) The reciprocal of \( \dfrac{0}{3}\) does not exist
(xi) The reciprocal of 1 is 1
Answered by Sakshi | 1 year agoBy what number should 1365 be divided to get 31 as quotient and 32 as remainder?
Which of the following statement is true / false?
(i) \(\dfrac{ 2 }{ 3} – \dfrac{4 }{ 5}\) is not a rational number.
(ii) \( \dfrac{ -5 }{ 7}\) is the additive inverse of \( \dfrac{ 5 }{ 7}\)
(iii) 0 is the additive inverse of its own.
(iv) Commutative property holds for subtraction of rational numbers.
(v) Associative property does not hold for subtraction of rational numbers.
(vi) 0 is the identity element for subtraction of rational numbers.
If x = \( \dfrac{4 }{ 9}\), y =\( \dfrac{-7 }{ 12}\) and z = \( \dfrac{-2 }{ 3}\), then verify that x – (y – z) ≠ (x – y) – z
If x = \(\dfrac{ – 4 }{ 7}\) and y = \( \dfrac{2 }{ 5}\), then verify that x – y ≠ y – x
Subtract the sum of \(\dfrac{ – 5 }{ 7} and\dfrac{ – 8 }{ 3}\) from the sum of \(\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}\)