\(\frac{2}{5} \times(-\frac{3}{7}) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5}\)
= \(\frac{2}{5} \times(-\frac{3}{7}) + \frac{1}{14} \times \frac{2}{5}-\frac{1}{6} \times \frac{3}{2}\) (By commutativity)
= \( \frac{2}{5} \times (-\frac{3}{7} + \frac{1}{14})- \frac{1}{4}\) (by distributivty)
=\( \frac{2}{5} \times (\frac{-3 \times 2 +1}{14}) - \frac{1}{14}\)
= \(\frac{2}{5} \times (-\frac{5}{14})-\frac{1}{4}\)
= \( \frac{1}{7}-\frac{1}{4}\)
=\( \frac{-4-7}{28} = \frac{-11}{28}\)
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 \(\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}\)