How to come up with unit rate for 1 day when give 1.5 days?

Question

Question: A gerbil drinks 2/3 of a water bottle every 1.5 days. Use a unit rate to discover how many water bottles the gerbil drinks in 5 days.

When given problems like this before, I have used whole numbers and was easily able to figure out a unit rate for 1 day. Since I have fractions, I am confused on how to break 1.5 down to 1 all while changing the 2/3.

When I did this problem without a unit rate, I multiplied 2/3 by 3 and discovered that the gerbil drank 2 water bottles in 4.5 days. I then took 1/2 of 2/3 and got that the gerbil drinks around 2.3 water bottles in 5 days!

How do I compute this using unit rates?

Answer 1

So we are given that the gerbil drinks $\frac{2}{3}$ bottles every $\frac{3}{2}$ days.

Hence, the amount it drinks in one day is $\frac{2}{3} \div \frac{3}{2} = \frac{4}{9}$ bottles.

Hence, the amount it drinks in five days is $\frac{4}{9} \times 5 = \frac{20}{9} = 2.\overline{2}$

The second step is the most important here: all you are doing is simple division, that gives you the unit rate.

Doing it your way, you said that $2$ liters are consumed in $4.5$ days. The remaining is $\frac{1}{3}$ of $\frac{3}{2}$ days, so the amount consumed in that time is $\frac{1}{3}*\frac{2}{3} = \frac{2}{9}$. Hence the answer is $2\frac{2}{9} = 2.\overline{2}$

By the way, feel free to clear doubts, I know it's a sensitive topic.

Answer 2

Simply write down an expression for the rate and extend the fraction so that the denominator is $1$:

The rate given is $\frac{2}{3} \text{ bottles per }\frac{3}{2} \text{ days.}$ Here "per" means "divided by", so we have $$\frac{\frac{2}{3}}{\frac{3}{2}}\text{ bottles per day}=\frac{4}{9} \text{ bottles per day} \implies 5\times \frac{4}{9} \text{ bottles per $5$ days}=\frac{20}{9} \text{ bottles per $5$ days}$$