Fractions and Mixed Numbers

0:00 Welcome to this explainer. Okay, we're jumping right into a topic today that makes a lot of people break into a cold sweat, mastering ASVAB fractions. Now, if you're gearing up for the ASVAB, you already know the deal. Calculators are strictly banned. You've got to do the math by hand or in your head. But seriously, don't worry. We are going to take a very patient step-by-step approach to building up your confidence. By the time we wrap up, you'll be able to tackle these fraction problems completely without a calculator, relying entirely on the foolproof strategies we're about to build together. Here is our game plan for today. We'll start with fraction basics, move on to core math operations, and then dive into our no calculator strategy. After that, we'll walk through some step-by-step worked examples, look at how to avoid common fraction traps, and finally, we'll do a check yourself practice so you can test your skills. All right, let's kick things off with section one. Fraction basics and really understanding the parts. Before we even think about calculating anything, we need to understand the actual anatomy of a fraction. The bottom number is your denominator.

1:02 Think of it as setting the rules. It tells you exactly how many equal parts make up one whole. The top number is your numerator, which simply tells you how many of those parts you're actually counting. So say a tank is three-fifths full. Mentally, the whole tank is divided into five equal bands, and three of them are filled. Makes sense, right? Now, a super crucial skill on the ASVAB is simplifying. Mostly because the answer choices are almost always going to be in their simplest form. To get there, you just divide both the top and the bottom by their greatest common factor. Look at 12 over 30. The absolute largest number that divides evenly into both 12 and 30 is six. Divide them both by six, and you get two fifths. They represent the exact same value just with smaller, way friendlier numbers. Core fraction math operations. We're talking add, subtract, multiply, and divide. Now that we've got our basic definitions down, let's look at addition. The biggest thing to remember is that fractions can only be added together when they count the exact same size parts. That means you absolutely have to find a common denominator first.

2:08 Take two-thirds plus one-sixth. We can't just mash those together. We have to convert two-thirds into four-sixth. Now that both fractions share a denominator of six, it's a breeze. We simply add the numerators straight across. Four plus one is five. Giving us our final answer of five-sixth. Subtraction? Well, it works the exact same way. You need that common denominator before you can do anything else. Here we have five-sixths minus three-eighths. The smallest number that both six and eight can divide into is twenty-four, so we convert five-sixths to twenty over twenty-four and three-eighths to nine over twenty-four. Subtract the numerators, twenty-minus-nine, and we get eleven-twenty-fourths. Honestly, multiplication is actually easier. For multiplication, you don't need a common denominator at all. You literally just multiply straight across. But here is the secret sauce for doing this without a calculator. Cancel out shared factors first to keep the numbers small. Take four-ninths times fifteen-sixteenths. Before multiplying, notice that the four on top and the sixteen on the bottom share a factor of four.

3:14 Cross them out, leaving a one and a four. Now look at fifteen and nine. They share a factor of three. Cross those out, leaving a five and a three. Suddenly, instead of big, messy numbers, we're just multiplying one-third by five-fourths, which smoothly gives us five-twelfths. Okay, now for division. The rule here is incredibly simple. It's just keep, change, flip. Keep the first fraction exactly as it is. Change the division sign to multiplication and turn only the second fraction upside down. So five-sixths divided by two-thirds becomes five-sixths times three-halves. Multiply straight across to get fifteen-twelfths. When we simplify that improper fraction, we get one and three-twelfths. And hey, that reduces perfectly down to one and one-fourth. Let's move to section three. Applications and our no-calculator strategy. This is where we build mental math mastery. Word problems on the ASVAB is really going to test you. But if you memorize these four simple rules, it makes the math totally manageable. First, simplify early and often.

4:18 Always cancel common factors before you multiply. Second, whenever a word problem asks for a fraction of something, 'of' is your trigger word to multiply. Third, always use the smallest common denominator you can find to save yourself from nasty, complex arithmetic. And fourth, estimate using benchmarks, like one-half or one, just to quickly check if your final answer even makes logical sense. All right, section four. Step by step worked examples. Let's put these strategies to work. Let's look at our first real example. Imagine two boards laid end to end. One is three and five eighths feet long. And the other is two and three quarters feet long. What's the total length? The phrases 'end to end' and 'total' Tell us right away this is an addition problem involving mixed numbers. So let's solve it together. We need a common denominator for the fractional parts. And eight works perfectly. We change two and three quarters into two and six eighths. Now add the whole numbers. Three plus two is five. Add the fractions. Five eighths plus six eighths is eleven eighths. But watch out.

5:21 Eleven eighths is an improper fraction. It's actually hiding another whole number inside it. So five and eleven eighths becomes six and three eighths feet. Let's look at another one. Say a cook has five cups of rice. Each serving uses two-thirds of a cup. How many full servings can be made? We're trying to figure out how many smaller pieces fit into a total, which means we need to set up a division problem. We set up five divided by two-thirds. Remember our keep-change-flip rule? So it becomes five times three halves. Five times three is fifteen, so we get fifteen halves. When we divide fifteen by two, we get seven with a remainder of one. So seven and a half. But look really closely at the original question. It asked for full servings. You can't hand someone a half serving and call it full. So the final correct answer here is exactly seven full servings. Avoiding common fraction traps. You definitely want to steer clear of these mistakes. Adding denominators. The test makers love setting this trap. Look at the left side. One-third plus one-fourth does not equal two-sevenths.

6:25 You can never ever just add denominators together. Because the parts are completely different sizes. You have to follow the right side. Rename them with a common denominator of twelve. Four-twelfths plus three-twelfths equals seven-twelfths. Do not fall for the trap on the left. Multiplying mixed numbers piece by piece. Look at the left. Two and a half times three and a third. You might be super tempted to just multiply the whole numbers to get six and the fractions to get one-sixth. Wrong. That completely leaves out parts of the math. Look at the right side. You must always convert them to improper fractions first. You get five halves times ten-thirds. Multiply straight across for fifty sixths. Simplify that down to twenty-five-thirds. And that ultimately gets you to eight and one-third. See? A totally different answer. All right. We've made it to section six. Check yourself practice. Time for a little independent practice to see how you're feeling. A repair crew has finished 24 of its 40 assigned work orders. What fraction is finished in simplest form? I want you to go ahead and pause this explainer right now. Grab a pencil and actually try solving this by hand before you hit play again.

7:31 Okay, we're back. The correct answer is three-fifths. Really great job if you realize that the initial fraction is twenty-four over forty. And then remembered our rule to find the greatest common factor. Both numbers divide evenly by eight. Twenty-four divided by eight is three, and forty divided by eight is five. Let's try one final question. A storeroom holds 64 batteries. If three-eighths of them are issued to a patrol, how many batteries are issued? Again, hit pause? Think really carefully about what the word 'of' triggers in a word problem and calculate your answer without using a calculator. All right, let's see how you did. The correct answer is 24 batteries. Since of means multiply, we needed to find three-eighths of 64. Our no calculator strategy tells us to divide by the denominator first to keep the numbers nice and small. 64 divided by eight is eight. Then just multiply that by the numerator. Eight times three equals 24 perfectly. Look at that. You just conquered ASVAB fractions entirely by hand, which kind of makes me wonder, with this step-by-step approach under your belt, what other math fears are you ready to conquer next?