Question
Simplify
$\frac{13}{11} \times \frac{-14}{5}+\frac{13}{11} \times \frac{-7}{5}+\frac{-13}{11} \times \frac{34}{5}$
$\frac{13}{11} \times \frac{-14}{5}+\frac{13}{11} \times \frac{-7}{5}+\frac{-13}{11} \times \frac{34}{5}$
✓
Answer
Given,
$\frac{13}{11} \times \frac{-14}{5}+\frac{13}{11} \times \frac{-7}{5}+\frac{-13}{11} \times \frac{34}{5}$
$\therefore$ Product of rational numbers $=\frac{\text { Product of numerators }}{\text { Product of denominators }}$
$=\frac{13 \times(-14)}{11 \times 5}+\frac{13 \times(-7)}{11 \times 5}+\frac{(-13) \times(34)}{11 \times 5}$
$=\frac{(-182)}{55}+\frac{(-91)}{55}+\frac{(-442)}{55}$
$=\frac{-182+(-91)+(-442)}{55}$
$=\frac{-715}{55}=\frac{-143}{11}$
$=\frac{-13}{1}=-13$
$\frac{13}{11} \times \frac{-14}{5}+\frac{13}{11} \times \frac{-7}{5}+\frac{-13}{11} \times \frac{34}{5}$
$\therefore$ Product of rational numbers $=\frac{\text { Product of numerators }}{\text { Product of denominators }}$
$=\frac{13 \times(-14)}{11 \times 5}+\frac{13 \times(-7)}{11 \times 5}+\frac{(-13) \times(34)}{11 \times 5}$
$=\frac{(-182)}{55}+\frac{(-91)}{55}+\frac{(-442)}{55}$
$=\frac{-182+(-91)+(-442)}{55}$
$=\frac{-715}{55}=\frac{-143}{11}$
$=\frac{-13}{1}=-13$
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