Mastering Oilers/Plant Tenders Exam Calculation Skills

If a bucket capable of carrying 5 3/4 cubic yards is loaded to 3/4 of its capacity, it will be carrying approximately __________ cubic yards.

• A. 3 3/4
• B. 4 1/4
• C. 3 1/4
• D. 5 1/4

Answer: (B)

To find out how much the bucket is carrying when loaded to 3/4 of its capacity, we need to perform a calculation based on the capacity of the bucket, which is 5 3/4 cubic yards. First, it is essential to convert 5 3/4 into an improper fraction. This is done by multiplying the whole number (5) by the denominator (4) and adding the numerator (3): 5 * 4 = 20 20 + 3 = 23 Thus, 5 3/4 is equivalent to 23/4 cubic yards. Next, we need to calculate 3/4 of 23/4. This involves multiplying the two fractions: (3/4) * (23/4) = (3 * 23) / (4 * 4) = 69 / 16 cubic yards. Now, to get a more understandable measurement, we can convert 69/16 back into a mixed number. Dividing 69 by 16 gives us 4 with a remainder: 69 ÷ 16 = 4 remainder 5. This means that 69/16 cubic yards is equal to 4 5/16 cubic yards. To find

When preparing for the Oilers/Plant Tenders (HHC) Civil Service Exam, math plays a crucial role, especially when you're dealing with measurement conversions. You know what? A lot of candidates find themselves scratching their heads over calculations, particularly those involving mixed numbers and fractions. Today, let’s break this down using an example that’ll show you just how easy it can be—in a fun kind of way!

Imagine you’ve got a bucket that can hold 5 3/4 cubic yards. If it’s loaded up to 3/4 of its capacity, how many cubic yards are we looking at here? A little numerical exercise, right?

First things first, let’s convert that mixed number, 5 3/4, into an improper fraction. Why? Because it makes calculations much simpler. Here’s how it goes:

• Multiply 5 (the whole number) by 4 (the denominator): 5 * 4 = 20.

• Then, add the numerator: 20 + 3 = 23.

So, 5 3/4 turns into 23/4 cubic yards. Pretty neat, right?

Now, let’s get to the juicy part—calculating 3/4 of that. You're going to multiply:

[

(3/4) * (23/4) = (3 * 23) / (4 * 4) = 69 / 16.

]

Whoa, hold on! What does 69/16 actually mean? Let’s do a little division dance:

When you divide 69 by 16, you get 4 as the whole number, and what’s left over? A remainder of 5. So that means 69/16 can be expressed as a mixed number, which comes out to be 4 5/16 cubic yards.

Isn’t it satisfying when you get the right answer? After crunching through these numbers, the options we have considered lead us straight to choice B: 4 1/4. But here's where it gets interesting—while 4 5/16 is the technical answer, checking against our available choices shows that the closest and most appropriate selection is indeed 4 1/4!

Whether you’re in a study group, preparing solo, or just honing those math skills that’ll make you a whiz come test time, remember that understanding the process is key. Familiarity with these concepts not only helps you ace your exam but equips you with the kind of practical skills that can be applied in the real world—like when your buddy needs help figuring out how much soil to buy for that DIY garden project.

So, roll up those sleeves, grab some practice problems, and let’s get calculating! By mastering fractions and mixed numbers, you’re not just preparing for an exam; you’re setting yourself up for future success—whether on the job or in daily life.