Question

Divide. Write your answer as a fraction or mixed number in simplest form.
− 5/12 ÷ - 15/16

Answer 1

To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction.

The problem is:

\[
-\frac{5}{12} \div -\frac{15}{16}
\]

This can be rewritten as:

\[
-\frac{5}{12} \times -\frac{16}{15}
\]

Since multiplying two negative fractions gives a positive result, we can remove the negatives:

\[
\frac{5}{12} \times \frac{16}{15}
\]

Next, multiply the numerators and the denominators:

\[
\frac{5 \times 16}{12 \times 15} = \frac{80}{180}
\]

Now, we simplify \(\frac{80}{180}\). First, find the greatest common divisor (GCD) of 80 and 180. The GCD is 20.

Now, divide both the numerator and the denominator by their GCD:

\[
\frac{80 \div 20}{180 \div 20} = \frac{4}{9}
\]

So, the answer is:

\[
\frac{4}{9}
\]