Asvab for dummies book pdf free download

Press ESC to close. Table of Contents. Additional Information:. PDF eBooks. Show Comments. Do the work in parenthesis. Division and multiplication come next in this problem, only multiplication is needed and no exponent work is present. Finally, do the addition and subtraction in this problem, only addition is needed. Your final answer is We think most mathematicians must have a sweet tooth.

If a whole number is a pizza, a fraction is a slice of pizza. A fraction also illustrates its relationship to the whole pizza. Can anyone say pig? The number above the fraction bar — the three slices your cousin ate — is called the numerator. The number written below the fraction bar — the total number of slices the pizza is divided into — is called the denominator.

Adding and subtracting fractions To add and subtract fractions, the fractions must have the same denominator, which is called a common denominator. There are two different methods to use.

Read on. Chapter 7: Arithmetic Reasoning Method one Finding a common denominator can be easy, or it can be as hard as picking off all the anchovies. This operation is an easy one, and you use this process whenever you can evenly divide one denominator by another. Follow the steps below: 1. Divide the larger denominator by the smaller denominator.

In this case, 10 can be divided evenly by 5. The quotient that results is 2. The result is Replace the denominator of the smaller fraction with the result from Step 2. Multiply the numerator of the smaller fraction by 2.

In this case, the result is 6. Replace the numerator with the result of the previous step. So you have to find a common denominator that both 5 and 6 divide into evenly: 1. Multiply the denominator of the first fraction by the denominator of the second fraction.

The common denominator for both fractions is Multiply the numerator by the number you used to multiply to result in the new denominator. To convert the denominator, 5, to 30, you multiply by 6, so multiply the numerator 3 by 6. Otherwise, you change the value of the fraction.

But if you had multiplied only the denominator by 6, you would have a new number. Now pause and take a bite of pizza. Another more complicated way of adding fractions is having multiple fractions to add. If you have more than two fractions with different denominators, you have to find a common denominator that all the denominators divide into.

A simple way to find a common denominator is to take the largest denominator in this case 5 and multiply it by whole numbers, starting with 1, 2, 3, 4, and so on until you find a denominator that the other denominators also divide into evenly. In this case, 30 is the first number you can find that 2, 3, and 5 can divide into evenly, so 30 is your common denominator. Multiplying and simplifying fractions Multiplying fractions is easy.

You just multiply the numerators and then multiply the denominators. Occasionally, when you multiply fractions, you end up with an extremely large fraction that can be simplified or reduced. A number that you can divide into both the numerator and the denominator is called a common factor. In this example, the common factor is 2. Dividing fractions Dividing fractions is simple if you remember this rule: Dividing a fraction by a number is the same as multiplying it by the inverse of that number.

Of course there are always exceptions. Zero has no inverse. No one knows why — it just is. To come up with the inverse of a number, simply stand the number on its head. Converting improper fractions to mixed numbers. Simply divide the numerator by the denominator. If you want to multiply or divide a mixed number, you need to convert it into a fraction — an improper fraction. To make the change, you convert the whole number into a fraction and add it to the fraction you already have.

To make a decimal into a percent, move the decimal point two spaces to the right and add a percent sign — 0. See the following sections for more thorough discussions of decimals and percents. The first space to the right of the decimal is the tenth place, the second space is the hundredth place, and the third is the thousandth and so on. Adding and subtracting decimals To add and subtract decimals, put the numbers in a column and line up the decimal points.

Then add or subtract as if the decimals were whole numbers, keeping the decimal point in the same position in your answer. Here are two examples: 1. In the above problems, 0. Multiplying decimals Multiplying a decimal is like multiplying a regular, everyday whole number, except that you have to place the decimal point in the correct position once you reach an answer.

To multiply decimals, start off by adding the number of decimal places from the right of the decimal point in the numbers being multiplied. Move the decimal point back to the left 3 places. The resulting product is For instance, 3 can also be expressed as 3. For instance, 3. Suppose your answer is 50, and you have to move the decimal point to the left three spaces. So you add a zero to the left, to make , and put the decimal point in its proper position:. Add the decimal places in the two numbers.

There are four. Then put the decimal point in the correct place in the answer. For , count from right to left four places, and put the decimal point there: 0. Move the decimal point over to the right until the decimal is a whole number, counting the number of decimal places.

Remember how many places you moved the decimal — you need that info later. Change 1. Chapter 7: Arithmetic Reasoning 3. Now move the decimal point two places to the left to make up for moving it two places to the right when you made 1.

Dividing decimals by decimals To divide a decimal by another decimal in which there are equal numbers after the decimal point, make the divisor the decimal going into the other number a whole number. Move the decimal point all the way to the right, counting the number of places you move it. Then move the decimal in the dividend the number being divided the same number of decimal places. So, if you want to divide 0. Move the decimal point two places to the right in the divisor: 0.

Move the decimal in the dividend the same number of spaces: 0. Divide 15 by The result is 0. If the dividend is a longer decimal than the divisor, you follow the same steps, but you have to add an extra step at the end. So, if your problem is 0. Move the decimal point in the divisor 0. Then move the decimal point in the dividend two places, to come up with Now the problem looks like this: Convert the first number Move the decimal point one place to the left to make up for moving it one place to the right when you converted The answer is 0.

When the divisor is a longer decimal than the dividend, such as 0. Then move the decimal the same number of spaces in the dividend, adding zeroes as needed: 0.

Playing with percents A percent is a fraction based on one hundredths. You need to be able to convert percents to fractions or decimals to answer these questions correctly. Moving the decimal point two spaces to the left leaves you with 0. Some fractions convert to repeating decimals — a decimal in which one digit is repeated infinitely.

It expresses a comparison by proportion. For example, if Margaret invested in her tattoo parlor at a ratio to her business partner Julie, then Margaret put in two dollars for every one dollar that Julie put in.

You drive for miles and then refill the tank with 15 gallons of gas. You can compute your gas mileage by comparing ratios. Time for a tune up! Remembering important rates The term rate has various meanings. It can mean the speed at which one works. John reads at the rate of one page per minute.

It can also mean an amount of money paid based on another amount. Word problems often ask you to solve problems concerning travel or simple interest rates. For example, a map drawn to scale may have a one-inch drawing of a road that represents one mile of physical road in the real world. The Arithmetic Reasoning portion of the ASVAB often asks you to calculate a problem based on scale, which can be represented as a ratio or a fraction.

On a map with a scale of one inch to one mile, the ratio of the scale is represented as The problem wants you to determine how many inches on the map represents miles, if 1 inch is equal to miles. You also know that x inches is equal to miles. Now all you have to do is solve for x. If this problem causes you to scratch your head, check out Chapter 8 for more information on mathematics. Almost every military job makes use of scales, which is why scale-related questions are so common on the ASVAB.

Completing a number series The Arithmetic Reasoning subtest often includes questions that test your ability to logically complete a series of numbers. And to do this, you must also be able to quickly perform mathematical operations. Suppose you have a series of numbers that look like this: 1, 4, 7, 10,? Each new number is reached by adding three to the previous number.

You may also see sequences like this: 1, 2, 3, 6,? In this sequence, the numbers are being added together. Some people, blessed with superior sequencing genes, can figure out patterns instinctively. The rest of the population has to rely on a more difficult, manual effort.

Finding a pattern in a series of numbers requires you to think about how numbers work. For instance, in the second example in the preceding section, seeing the number should alert you that multiplication is the operation because is so much larger than the other numbers.

Because the numbers in the series both increase and decrease as the series continues, you should suspect that something tricky is going on. In the beginning of this chapter, we mention that you should be supplied with some scratch paper.

Make sure to use it! Plus, by following the tips in this section, you can do a better job of guessing correctly and increase your odds of winning the lottery, er, we mean scoring well on the ASVAB. If you do, you may not have time to finish this subtest. But, before you commit to an answer to a math question, double-check your calculations.

One easy way to double-check your work is to plug the answer into the question. Logical deductions: Eliminating unlikely answers Check out the sand-in-the-box problem below. How many cubic inches of sand does a cardboard box measuring inches long by inches wide by inches tall contain? A 52 cubic inches B 88 cubic inches C cubic inches D 1, cubic inches Chapter 7: Arithmetic Reasoning You may have already shrewdly determined that the question is asking you to find the volume of the cardboard box.

In fact, you think that the only time anyone told you about volume was when they said that your stereo was too loud, which is no help to you now. Still all is not lost. If you use logic, you may be able to eliminate some incorrect or unlikely answers from the choices, which improves your chances of guessing correctly.

Check out the following thought process: 1. So you continue thinking about the problem. You know that if you multiply the height of the box by its length, you get the area, not the volume.

Therefore Choice C is also wrong. At this point, it may occur to you that if you multiply the height of the box by its length and by its width, you get its volume. Or it may not occur to you. But you do know that the volume measurement is going to be greater than the area measurement.

So you can choose an answer that is larger than the area of the cardboard box. Therefore, if Choice C , , is too small, then Choice B , 88, is also too small — and also wrong. So the correct answer is D , Then you can choose among the remaining answers.

Doing this means you have a greater chance of guessing the right answer. Avoiding testing traps: Complete the whole problem!

Sometimes those crafty test makers set little traps for you to fall into. How many 4-xinch shingles are needed to cover a roof that measures 12 x 16 feet? A B 12 C 27, D 1, This question asks you to perform several operations. You must determine the area of the roof, figure out the area each shingle will cover, and then come up with the total number of shingles required to cover the area of the roof.

I know how to answer this one! The measurements must be converted so the area of the shingles and the area of the roof are both expressed in the same measuring unit. The easiest way to figure out this problem is to multiply both the length and the height of the roof by 12 because 12 inches are in a foot and then multiply the height and the length of the roof together to determine the total area of the roof in inches.

Thus, the area of the roof in inches is 27, Some people, pleased that they remembered to convert feet into inches, choose Choice C. To determine the number of shingles needed, divide 27, by 16 the area in inches of each shingle to come up with 1, shingles or enough to cause John to go back to the shop for a heavy-duty pickup truck. Correct answer: Choice D. Use your common sense!

Go back and try again. Remember, this subtest tests your ability to make calculations based on real-life problems, and no real-life roof was ever covered with only 12 shingles.

Many people have a hard time with them. You not only have to foster a talent for analyzing the problem and picking out the essential information, but also you need a solid foundation in basic math skills. I assure you mine are far greater. Okay, just kidding.

This subtest asks questions about basic high school mathematics. No college or graduate degrees needed. The Mathematics Knowledge subtest consists of 25 questions, and you have 24 minutes to complete the subtest.

You have to focus and concentrate to solve each problem quickly and accurately. And no calculators allowed! The vast majority of questions on this subtest are expressed in mathematical terms, but you may see some word problems as well.

Generally, such word problems are more direct than the problems you see on the Arithmetic Reasoning subtest see Chapter 7. But most of the time, the Mathematics Knowledge subtest only contains one or two questions testing each specific mathematical concept. For example, one question may ask you to multiply fractions, the next may ask you to solve a mathematical inequality, and the question after that may ask you to find the value of an exponent. These concepts are covered in this chapter.

All this variety forces you to constantly shift your mental gears to quickly deal with different concepts. You can look at this situation from two perspectives. These mental gymnastics can be difficult and frustrating, especially if you know everything about solving for x but nothing about deriving a square root. But variety can also be the spice of life.

To qualify for certain jobs in the military, you have to score well on the Mathematics Knowledge subtest. You also have to do well on this subtest which is part of the AFQT discussed in Chapter 1 in order to enlist. Turn to the Appendix to find out more about the subtest scores needed for specific military jobs. So 6 factorial 6! A factorial helps you determine permutations — all the different possible ways an event might turn out.

For example, if you want to know how many different ways six runners could finish a race permutation , you would solve for 6! Get the idea? For example, the square root of 36 is 6. If you square 6, or multiply it by itself, you produce You perform rounding operations all the time — often without even thinking about it. Often, numbers are rounded to the nearest tenth.

For any number 5 and over, round up; for any number under 5, round down. For example, 1. Many math problems require rounding. Algebra Review Some people may freak out just hearing the word algebra. But in actuality, algebra is just a way to put problems into mathematical language using the simplest mathematical terms possible. The unknown is the answer you want find. You can express this missing piece of information in an equation as well: x how much it will cost to buy a superduper size equals 3 the cost increase times p the price of one regular sized drink.

You can remove the multiplication symbol in algebraic expressions when using a combination of letters and numbers. The multiplication symbol is implied. The letters in an algebra problem are commonly called variables, meaning that the number they stand for varies or changes. Algebra-related terms Special algebra terms are used to describe how numbers function and how they relate to each other.

Examples of composite numbers are 6, 8, and 9. To factor a composite number, you simply determine the numbers that you can divide into it. For example, 8 can be divided by the numbers 2 and 4 in addition to 1 and 8 , so 2 and 4 are factors of 8. Check out the definition of factor a bit earlier in this list. Examples of prime numbers are 2, 5, and In all these cases, the quantities are the same on both sides of the equal sign.

So far, so simple, so good. To get that job done, you have to move any other numbers on the x side of the equal sign to the other side of the equal sign. To move the number on the x side to the opposite side, you have to perform the inverse operation.

The inverse operation of addition is subtraction. For a full rundown on inverse operations, check out Chapter 7. You can perform any calculation on either side of an equation as long as you do it to both sides of the equation. That keeps the equation equal. Multiplying and dividing using integers An integer is any positive or negative whole number or zero. In multiplication and division, if the two terms being operated on on either side of the equal sign are both positive numbers or both negative numbers, the answer is a positive number.

If one number is negative and the other is positive, the answer is negative. In an algebra equation, if the same letter is used more than once, it stands for the same number. Solving multistep equations Not all algebra problems have one-step solutions. An example of a multistep equation is when x shows up on both sides of the equal sign. Then you have to get rid of x from one side of the equation by moving an x from one side to the other.

You do this by performing the inverse operation. Perform the subtraction operation. To finish solving the problem, subtract 3 from each side of the equation.

Divide both sides of the equation by 2. Explaining exponents Exponents are an easy way to show that a number is to be multiplied by itself a certain number of times. A note about scientific notation Scientific notation is a compact format for writing very large or very small numbers. While its most often used in scientific fields, you may find a question or two on the Mathematics Knowledge subtest of the ASVAB, asking you to covert a number to scientific notation or vice-versa.

Scientific notation separates a number into two parts: a decimal fraction, usually between 1 and 10, and a power of ten. Therefore 1. Take the number 36, for example. One of the factors of 36 is 6. The number 36 has other factors such as One number can only have one square root. The sign for a square root is called the radical sign. To find the square root of a number without a calculator, make an educated guess and then verify your results.

To use the educated-guess method, you have to know the square roots of a few perfect squares. Multiply 7. Try multiplying 7. Exponential roots The wonderful world of math is also home to concepts like cube roots, fourth roots, fifth roots, and so on.

These roots are a factor of a number, which, when cubed multiplied by itself three times , taken to the fourth power multiplied by itself four times , and so on, produce the original number. Any guesses? You want a more specific explanation of geometry than that? Okay, geometry is the branch of mathematics concerned with measuring things and defining the properties of and relationships between and among shapes, lines, points, angles, and other such objects.

Outlining angles Angles are formed when two lines intersect at a point. Angles are measured in degrees. Take a look at the different types of angles in Figure The sides of a triangle are called legs. Check out Figure to see what these triangles look like. Sides A, B, C are equal.

Angles 1, 2, 3 are equal. See Figure for the illustration of these quadrilaterals. Figure An illustration of quadrilaterals. Square Rectangle Parallelogram Rhombus Trapezoid To determine the perimeter of a quadrilateral, simply add the length of all the sides. Going around in circles A circle is formed when the points of a closed line are all located equal distances from its center. The closed line of a circle is called its perimeter or circumference. The radius of a circle is the measurement from the center of the circle to any point on the circumference of the circle.

The diameter of the circle is measured as a line passing through the center of the circle, from a point on one side of the circle all the way to a point on the other side of the circle. See Figure , which shows you the parts of a circle. Why 4. Remember, the radius is always half the diameter, and the diameter is 9 inches. You can think of volume as how much a shape would hold if you poured water into it. Volume is measured in cubic units. This is possible because the length, width, and height of a rectangle are consistent throughout the whole shape.

That would make it a breeze. In this section, you come up to speed on how to solve problems that the Mathematics Knowledge subtest commonly throws at its victims, um, test takers. Factoring to find original numbers Now and then, the ASVAB gives you a product the answer to a multiplication problem , and you have to find the original numbers that were multiplied together to produce that product.

This process is called factoring. You use factors when you combine like terms and add fractions. Find the highest common factor — the highest number that evenly divides all the terms in the expression.

In this case, the highest number that divides into both terms is 2. Then figure out the common factors for the variables too. In this case, the highest variable that divides into both xy and x2 is x. Okay — take what you know to this point, and you can see that the highest common factor is 2x. So far, so good. Now divide 2x into both terms in the expression. Finally, multiply the entire expression by 2x to set the equation equal to its original value. Time to try something a little more complicated: factoring a trinomial a problem with three terms.

Find the factors of the first term of the trinomial. Put those factors x and x on the left side of two sets of parentheses: x x 2. Determine whether the two expressions will be positive or negative. That means the resulting factors must be either plus or minus, because two pluses result in a positive number and two minuses result in a positive number. Because the second term —12x is a negative number, both of the factors must be negative. Because two negative numbers multiplied equals a positive number.

Plug the two numbers into the right side of the parentheses. This part can be tricky. The factors of the third term, when added or subtracted together must equal the second term of the trinomial. Making alphabet soup: The quadratic equation Algebra questions often ask you to solve for x or solve for an unknown.

You simply isolate the unknown on one side of the equation and solve the other side to learn what x equals. In this case, x equals 5. Sounds a little scary, huh? The Mathematical Knowledge subtest may ask you to solve one of these equations, but have no fear. This section can help. A quadratic equation is an equation that includes the square of an unknown.

The exponent in these equations is never higher than 2 because it would then no longer be the square of an unknown, but a cube or something else. First get rid of the pesky 7 by dividing both sides by 7. Using the square root rule, you then take the square root of both sides of the equation.

Just like with equations, the solution to an inequality is a value that makes the inequality true. For the most part, you solve inequalities the same as you would solve a normal equation. There are some facts of inequality life you need to keep in mind, however.

Knowing what the question is asking This subtest presents most of the questions as straightforward math problems, not word problems, so knowing what the question is asking you to do is easier. Finally, make sure you do all the calculations needed to produce the correct answer. Or, in a rush, you could multiply 9 the square root of 81 by 2 instead of squaring it, as the exponent indicates you should. Or, you might just multiply 81 by 81 to get 6, without remembering that you also need to then find the square root, which gives you the correct answer: Choice C.

So make sure you perform all the operations needed and that you perform the correct operations to find the right answer. Right out of the gate, read the question carefully. Some questions can seem out of your league at first glance, but if you look at them again, a light may go on in your brain. Suppose you get this question: s number of students are in a classroom. How many privates are in the audience? Solve for an unknown, s. See Chapter 6 for a refresher on multiplying fractions.

Solving what you can and guessing the rest Sometimes a problem requires multiple operations for you to arrive at the correct answer. You can still narrow your guess down by doing what you can. You can even make a pretty design on your answer sheet and still have a one-in-four chance of getting each answer right. With this pearl of wisdom in mind, you can see that Choice B , which adds 0. It also means that Choice D , which multiplies 0.

You have six places to make up, so move the decimal from Suppose you run across this question: A child is building a tower of blocks. Each block is a cube. Some blocks are white, and some blocks are red.

Red blocks surround each white block. How many red blocks surround each white block? This problem may be difficult to figure out until you sketch a six-sided block a cube on your scratch paper and realize that the block must be surrounded by six other blocks. Sometimes drawing that visual helps you solve the problem. Using the process of elimination Another method besides guessing you can use when you run into questions where you draw a total blank is to plug the possible answers into the equation and see which one works.

You may be able to solve the next question easily. So double-check your answers before putting your pencil down or before going on to the next problem on the computer. Then move along, private! You should use the old-fashioned way on these practice questions, too. Tell you what. A stellar performance can also help you get grants and bonuses for school, so—no pressure!

But don't be daunted: like any military operation, having the right plan of attack and equipment are key—and as the number-one-selling guide year after year that's packed with all the information you need to win, the latest edition ASVAB For Dummies takes care of both of these in one!

In a friendly, straightforward style, Angie Papple Johnston—who passed the test herself in to join the Army—provides in-depth reviews of all nine test subjects. You'll also get tips on how to pinpoint areas where you need to develop mental muscle and to strengthen your test-taking skills. And if this weren't already giving you some pretty awesome firepower, you can also go online to reinforce your game using flashcards and customizable practice tests calibrated to address areas where you need help the most.

Whatever your aim for your military career, this book provides the perfect training ground for you to be the very best you can be on the day of the test!