Question

evaluate using suitable properties (mention the properties)
$\frac{8}{9} \times \frac{4}{5} + \frac{5}{6} - \frac{9}{5} \times \frac{8}{9}$
evaluate using suitable properties( mention the properties)
$\frac{ - 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times \binom{ - 14}{9}$
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Answer 1

Step-by-step explanation:

1. $\frac{8}{9} \times \frac{4}{5} + \frac{5}{6} - \frac{9}{5} \times \frac{8}{9}$

$= \dfrac{8\cdot 4}{9\cdot 5} + \dfrac{5}{6} - \dfrac{9\cdot 8}{5\cdot 9}$ [By the $BODMAS$ acronym, we do Multiplication first]

$= \frac{32}{45}+\frac{5}{6} - \frac{8}{5}$ [In the third term, we multiplied $\frac{1}{9}$ in the fraction to cancel out $9$]

$= \dfrac{32\cdot 2 + 5\cdot 15 - 8\cdot 18}{90}$ [By simple arithmetic rules, we find the least common multiple of the denominators, divide it by the denominator of each term and multiply the numerator by the quotient]

$= \dfrac{64 + 75 - 144}{90}$

$= \dfrac{-5}{90}$ [Simplifying the expression]

$= \boxed{\dfrac{-1}{18}}$ [Multiply $\frac{1}{5}$ in the fraction to cancel out common factors]