= \( -\frac{2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}\)
= \( \frac{2}{3} \times \frac{3}{5} - \frac{3}{5} \times \frac{1}{6} + \frac{5}{2}\)
(using commutativity of rational numbers)
= \( (-\frac{3}{5})\times (\frac{2}{3} + \frac{1}{6}) + \frac{5}{2}\)
= \( (\frac{-3}{5}\times\frac{2\times 2 + 1}{6})+ \frac{5}{2} = (-\frac{3}{5}) \times \frac{5}{6} + \frac{5}{2}\)
= \( (-\frac{3}{6}) + \frac{5}{2} = (\frac{-3 + 5\times 3}{6}) = (\frac{-3 + 15}{6})\)
= \(\frac{12}{6} = 2\)
2 years 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 \(\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}\)