Mastering Fractions: A Smart Approach to College Math Placement Tests

When you’re gearing up for your College Math Placement Test, having a solid grasp of fractions can make a world of difference. So, let’s break down a specific example to demystify the process, shall we? The task at hand is to add 5 1/2 and 3 9/10. Sounds straightforward, right? But what if I told you that understanding how to convert mixed numbers to improper fractions is the key to easily solving more complex problems?

Let’s do it step by step, so you can feel confident tackling similar questions on your test. First off, let’s convert 5 1/2 into an improper fraction. Here’s the formula: Multiply the whole number (which is 5) by the denominator (which is 2). So, 5 times 2 gives us 10. Now, add the numerator (1) to that total: 10 plus 1 equals 11. Therefore, 5 1/2 can be written as the improper fraction 11/2.

Pretty simple, right? Now, let's shift gears and convert 3 9/10. The same process applies here. Take the whole number, 3, and multiply it by the denominator, 10: 3 times 10 is 30. Next, add the numerator (9) to give you 39. Voilà! You now have 3 9/10 as the improper fraction 39/10.

Now here’s the crucial part: to add these two fractions, we need a common denominator. The least common multiple of our denominators—2 and 10—is 10. So, we’ll convert 11/2 to have a denominator of 10. This is called scaling—you're essentially resizing the fraction while keeping its value the same. Multiply the numerator and denominator of 11/2 by 5. So, 11 times 5 gives you 55, and 2 times 5 gives you 10. Thus, we have 55/10.

With both fractions aligned, we can finally add!

55/10 + 39/10 = (55 + 39)/10 = 94/10.

But hold on, we aren’t finished just yet! This fraction can be simplified. If you divide the numerator and the denominator by 2, you get 47/5. And if we convert that back into a mixed number, we need to divide 47 by 5: it goes 9 times with a remainder of 2, which gives us 9 2/5.

And there you have it! The answer to our original question is B: 9 2/5.

So, next time you encounter a problem involving the addition of mixed numbers, remember: conversion is your best friend. Being thorough and methodical not only eases the process but also reinforces your understanding. Trust me, these skills will serve you well during your math placement test and beyond. Plus, who doesn’t love that satisfying a-ha moment when pieces of the puzzle finally click into place?

Before we wrap things up, let’s reflect on this: don’t just memorize these steps—understand them. Math is a language, and once you grasp the vocabulary, it gets a lot easier to have those enlightening conversations with your formulas.