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Simplify these fraction products.

Solution

Multiplying numerators gives $10\text{,}$ and multiplying denominators gives $21\text{.}$ The answer is $\frac{10}{21}\text{.}$

Before we multiply fractions, note that $\frac{12}{3}$ reduces to $4\text{,}$ and $\frac{15}{3}$ reduces to $5\text{.}$ So we just have $4\cdot5=20\text{.}$

Multiplying numerators gives $28\text{,}$ multiplying denominators gives $15\text{,}$ and multiplying a negative times a positive results in a negative. The answer is $-\frac{28}{15}\text{.}$

Before we multiply fractions, note that $\frac{12}{-20}$ reduces to $\frac{-3}{5}\text{.}$ So we have $\frac{70}{27}\cdot\frac{-3}{5}\text{.}$ Both the numerator of the first fraction and denominator of the second fraction are divisible by $5\text{,}$ so it helps to reduce both fractions accordingly and get $\frac{14}{27}\cdot\frac{-3}{1}\text{.}$ Both the denominator of the first fraction and numerator of the second fraction are divisible by $3\text{,}$ so it helps to reduce both fractions accordingly and get $\frac{14}{9}\cdot\frac{-1}{1}\text{.}$ Now we are just multiplying $\frac{14}{9}$ by $-1\text{,}$ so the result is $-\frac{14}{9}\text{.}$