**Math Knowledge may not be your thing. Very few people get excited about fractions and algebra – let alone square roots. But unless you know math vocabulary for the ASVAB exam, you can never get off on the right start.**

Math vocabulary is the license that allows you to correctly interpret questions. If you do not know what a question is asking, how can you possibly put together a path to solve it?

Today, that’s precisely the question we answer: learning the technical vocabulary that make-up so many **ASVAB math knowledge questions**. Remember, the standard of math is not the highest. You are not expected to learn degree-level math. Instead, this is high-school math level – much of which you may already have encountered.

Math Knowledge is one of the four subtests used to calculate your AFQT score – the score used to establish whether you are eligible to enlist in the US military.

There is no wiggle room, then.

You must score high.

And that begins with learning ASVAB math vocabulary:

**Exponents****Bases****Reciprocals****Integers****Factors****Square Roots****Factorials****Rounding**

Exponents are one of the must-know math vocabulary for the ASVAB exam to know. ASVAB test questions involving exponents are common. **Exponents **are used to identify the multiplication of a given number.

Examples: 15^{2}, 18^{3}, 4^{2}

The small number is known as the exponent. Therefore, in the first example, 15^{2} is the same as 15 x 15. This can also be phrased as “15 **squared**” or “15 to the second-power”.

Similarly, 18^{3} is a short-hand method of writing 18 x 18 x 18. When the exponent is three, we can also phrase this as, “18 **cubed**” or “18 to the third-power”.

Always remember you can add and subtract exponents that have the same **base number**. In the examples above, 15 and 18 and 4 are the base numbers and the small 2, 3, and 2 are the exponents.

Reciprocal numbers are fractions that can be multiplied by each other to produce a value of 1.

Sounds complicated, but it is quite simple!

Remember that any whole number – such as 1, 7, or 12 – can always be written in fraction form. For instance, 7 is the same as:

7 = 7/1

Now, the reciprocal of a fraction is itself turned upside-down. So in our example, the reciprocal of:

7/1 = 1/7

Remember the definition of a reciprocal: fractions that can be multiplied by each other to produce 1. And this is true in our example, namely:

7/1 = 1/7 …and when we multiply these two fractions, the answer is 1.

Similarly:

- The reciprocal of 4/9 is
**9/4**. - The reciprocal of 5 is
**1/5**. - The reciprocal of 2/5 is
**5/2**.

Integers are whole numbers. Nothing complex about integers whatsoever; one of the simplest math vocabulary for the ASVAB exam to learn.

Examples of integers include any whole number – such as:

**4****7****-11****67****1,245**

Integers can be either positive or negative!

Factors are numbers that can be divided equally into another number.

For example, take the number 6.

Examples of factors of 6 include:

**2****3**

2 can divide equally into 6, and 3 can divide equally into 6. Therefore, both these numbers are **factors** of six.

*Can you think of any other factors of six?*

Depending on how many factors a number has, it is referred to as either a composite number or a prime number:

**Composite numbers**have more than two factors. In the case of 8, for example, its factors are 2, 4, 1, and 8. Because 8 has more than 2 factors it is known as a composite number.**Prime numbers**have only two factors: itself and 1. For example, 2 is a prime number because it only has two factors: itself (2) and 1.

In terms of the question above regarding other factors of six, the correct answer is 6 and 1. Therefore, because 6 has four factors (2, 3, 1, and 6), it is an example of a composite number.

The square root of a number is the number which, when multiplied by itself, returns the original number.

For instance, 9 x 9 = 81. Therefore, the square root of 81 is 9.

**What is the square root of 36?**6, because 6 x 6 = 36.**What is the square root of 49?**7, because 7 x 7 = 49.

The symbol for the square root of a number is as follows:

√36 = 6

Therefore, the square root of a number (in this case 36) is the number needed to be multiplied by itself to produce the original number.

Factorials are used in probability to establish **permutations** – that is to say, the number of possible unique outcomes.

For example, imagine there are 8 motorcars in a race. The possible permutations of that race – for example: who comes 1st, 2nd, 3rd etc. – can be calculated using factorials.

The symbol for factorials is the exclamation point **!**.

Therefore, **8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320**

In other words, there are 40,320 **permutations** (not combinations!)of results of these 8 motorcars – in terms of who places 1^{st}, 2^{nd}, 3^{rd} etc. – in the race. Therefore, you have a 40,320 to 1 chance of correctly guessing the unique correct order.

We do not say “**combinations**” because each motorcar is unique. For example: if we had 4 numbers – 1, 2, 3, 4 – combinations can include one of these numbers being used more than once: 1123, for example. But in the case of a motorcar race, we cannot have a duplicate motorcar winner winning 2 positions, 2nd and 3rd, at the same time.

As we have learned, when you see the factorial symbol ! – you only need to multiply down from that number. See the example above with 8, how we multiply down until we arrive at 1.

At that point, we simply need to complete multiplication and this will give us the answer.

Rounding is the process of arriving at a simpler number by limiting the number of decimal places, or by having no decimal places at all.

Imagine you are asked the following question:

**Round 1.59 to the nearest whole number.**

Whole numbers are the same as integers: 6, 7, 1, 14 etc. Therefore, because the number after the decimal point is a 5, we round the number up to 2. Therefore, the correct answer is 2.

If the number is 1.41, the rounded answer would be 1 – because the number after the decimal point (4) is less than 5.

You may also be asked to round to 1 decimal place. For example: take the number 1.67. In this case, we need to focus on the second decimal (7), which is greater than 5, and so we round the number up to 1.7. The 7 here in the answer constitutes what the question asked us to do: to round to **one decimal place**.

Math operations do not need to be difficult.

As with any subject, it often comes down to the language used. If you know math vocabulary for the ASVAB exam, it makes **questions much easier to answer**. You will know what the question is asking, and you will develop a path to the solution.

It is not good enough to “sort-of” understand the concepts. Instead, you must have a fluent comprehension of these definitions and what these definitions are asking you to do in ASVAB math knowledge questions.

And by committing these math concepts to memory, you have just gone one step further toward exam success.

**We hope you found this ASVAB study guide helpful! Check back to our ASVAB Test Practice blog soon for more exclusive tools to help you master the exam and make it through to boot camp.**

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