Question

a. find the products. write your answers in simplest form.
-\frac{4}{5}\times(-\frac{5}{8})=
(-\frac{3}{10})\times(\frac{2}{3})=
the height of a 9 - inch candle changes at a rate of -\frac{2}{3} inch per hour when it is burning. how long will it take the candle to burn completely?
show your work.

Explanation:

Step1: Multiply fractions in part a

Multiply numerators and denominators.
$\frac{-4}{5}\times(-\frac{5}{8})=\frac{(- 4)\times(-5)}{5\times8}=\frac{20}{40}$

Step2: Simplify the result of part a

Reduce the fraction.
$\frac{20}{40}=\frac{1}{2}$

Step3: Multiply fractions in part b

Multiply numerators and denominators.
$(-\frac{3}{10})\times(\frac{2}{3})=\frac{(-3)\times2}{10\times3}=\frac{-6}{30}$

Step4: Simplify the result of part b

Reduce the fraction.
$\frac{-6}{30}=-\frac{1}{5}$

Step5: Solve for time of candle - burning

Let $t$ be the time in hours. The rate of burning is $\frac{2}{3}$ inches per hour and the initial height is 9 inches. We set up the equation $\frac{2}{3}t = 9$. Solve for $t$ by multiplying both sides by $\frac{3}{2}$.
$t=9\times\frac{3}{2}=\frac{27}{2} = 13.5$ hours

Answer:

a. $\frac{1}{2}$
b. $-\frac{1}{5}$
It will take 13.5 hours for the candle to burn completely.