Question

Help please these are killing my brain

Answer 1

How many gallons of milk are used each day? $10 \div 3$

How many days does it take to use 1 gallon of milk? All the other options.

First of all, note that options 1, 2, 4 and 5 are all the same: options 1 and 2 are the same because the multiplication is commutative, so we have

$\frac{1}{10}\times 3 = 3 \times \frac{1}{10} = \frac{3}{10}$

Also, "one tenth of three" means to multiply the fraction 1/10 and the number 3. So, it's exactly option 1. Finally, $3 \div 10$ is again the same fraction, except it's written in one line.

Now, since we know that it takes three days to consume 10 gallons, it means that in one day you consume $\frac{10}{3}$ gallons, assuming the rate is constant.

Similarly, if 10 gallons are consumed in 3 days, one gallon is consumed in $\frac{3}{10}$ days, assuming the rate is constant.

In other words, you have aggreagate informations, and you want unit information. If you want unit information with respect to the time, you divide by the amount of time. Vice versa, if you want unit information with respect to the quantity, you divide by the amount of that quantity (gallons of milk, in this case).