OKay, I know this is a homework question, but I am the dad and I really need to know the proceedure for this!
Here's the question:
One out of every 62.4 batteries is defective. If a company makes 374,400 batteries a day, how many are defective?
I'd like to have the process to get the answer too. Meaning I want to know the steps to solve the problem.
On
You can solve this with simple multiplication. Since one out of $62.4$ batteries is defective, the fraction representing the number of defective batteries is $\frac1{62.4}$. You multiply this by the total number of batteries, which gets you the following equation:
$$ \frac1{62.4} * 374,400=x$$
$$\frac{374,400}{62.4}=x$$
$$6000=x$$$x$ is the total number of batteries.
Divide $374400$ by $62.4$. That's literally all there is to it, on average.
Slight elaboration: You're given a number of batteries per day. You're also given a defect rate in batteries per defect. If you divide the former by the latter, you'll get defects per day. We can see this more viscerally, perhaps, in the units conversion:
$$ \frac{374400 \text{ batteries}}{\text{day}} \div \frac{62.4 \text{ batteries}}{1 \text{ defect}} = \frac{N \text{ defects}}{\text{day}} $$
Your desired answer is $N$.
If there were some other number $k$ defects per $62.4$, you would write
$$ \frac{374400 \text{ batteries}}{\text{day}} \div \frac{62.4 \text{ batteries}}{k \text{ defects}} = \frac{N \text{ defects}}{\text{day}} $$
so you'd have to divide $62.4$ by $k$ to get the number of batteries per single defect, and then divide $374400$ by that first result to get your final answer. That turns out to be the same as dividing $374400$ by $62.4$ (as we did previously when $k = 1$), and then multiplying it by $k$. Try it!