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Devide the sum of $-\frac{10}{9}$ & $\frac{11}{8}$ by the product o $-\frac{1}{4}$ & $\frac{24}{7}$

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Solve two-step linear inequalities

Full solution

Q. Devide the sum of

-\frac{10}{9}

&

\frac{11}{8}

by the product o

-\frac{1}{4}

&

\frac{24}{7}

Add Fractions: First, let's add the two fractions, $-\frac{10}{9}$ and $\frac{11}{8}$ . To do this, we need a common denominator, which is $72$ ( $9 \times 8$ ). So, we convert $-\frac{10}{9}$ to $-\frac{80}{72}$ and $\frac{11}{8}$ to $\frac{99}{72}$ . Now, we add them: $-\frac{80}{72} + \frac{99}{72}.$
Find Divisor: After adding the fractions, we get $\frac{19}{72}$ . Now we need to multiply $-\frac{1}{4}$ by $\frac{24}{7}$ to find the divisor. $-\frac{1}{4} \times \frac{24}{7} = -\frac{24}{28}$ . But we can simplify $-\frac{24}{28}$ to $-\frac{6}{7}$ by dividing both numerator and denominator by $4$ .
Divide Fractions: Now we divide $\frac{19}{72}$ by $-\frac{6}{7}$ . $\newline$ To divide by a fraction, we multiply by its reciprocal. $\newline$ So, we multiply $\frac{19}{72}$ by $-\frac{7}{6}$ . $\newline$ $\frac{19}{72} \times -\frac{7}{6} = -\frac{133}{432}$ .

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