6. Mathematics Knowledge

Question 1

What is an integer?

Answer 1

An integer is any positive or negative whole number or zero. The ASVAB often requires you to work with integers, such as -6, 0, or 27.

Question 2

What are numerical factors?

Answer 2

Numerical factors are integers (whole numbers) that can be divided evenly into another integer. To factor a 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. The prime factorization of the number 30 is written 2x3x5.

Question 3

What is a composite number?

Answer 3

A composite number is a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers; in other words, it has more than two factors. Examples of composite numbers are 6 (whose factors are 1, 2, 3, 4, 6, and 12).

Question 4

What is a prime number?

Answer 4

A prime number is a whole number that can be divided evenly by itself and by one but not by any number, which means that it has exactly two factors. Example, 11 (whose factors are 1 and 11)

Question 5

What is a base?

Answer 5

A base is a number that’s used as a factor a specific number of times—it’s a number raised to an exponent. For instance, the term 4³ (which can be written 4 x 4 x 4, and in which 4 is a factor three times) has a base of 4.

Question 6

What is an exponent?

Answer 6

An exponent is a shorthand method of indicating repeated multiplication. For example, 15 x 15 can also be expressed as 15², which is also known as “15 squared” or “15 to the second power.” The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the base by itself. Note that 15² (15x15), which equals 225, isn’t the same as 15 x 2 (which equals 30).

To express 15 x 15 x 15 using this shorthand method, simply write it as 15³ (which equals 3,375) isn’t the same as 15 x 3 which equals 45.

Question 7

What is the square root?

Answer 7

The square root of a number is the number that, when multiplied by itself (in other words, squared), equals to the original number. For example, the square root of 36 is 6. If you square 6, or multiply six by itself, you produce 36.

Question 8

What is a factorial?

Answer 8

A factorial is an operation represented by an exclamation point (!). You calculate a factorial by finding the product of (multiplying) a whole number and all the whole numbers less than it down to 1. That means 6 factorial (6!) is 6 x 5 x 4 x 3 x 2 x 1 = 720.

Question 9

What is a reciprocal?

Answer 9

A reciprocal is the number by which another number can be multiplied to produce 1; if you have a fraction, its reciprocal is that fraction turned upside down. For example, the reciprocal of 3 is ⅓. If you multiply 3 times ⅓, you get. The reciprocal of 1/6 is 6/1 (which is the same thing as 6); 1/6 x 6 = 1. The reciprocal of ⅔ is 3/2. The number 0 doesn’t have a reciprocal.

Question 10

What is rounding

Answer 10

Rounding is limiting a number to a certain number of significant digits (replacing some digits with zeros). If the number you’re eliminating is 5 or over, round up; for any number under 5, round down.

Question 11

What is an inverse operation?

Answer 11

Inverse operations are the opposite operation of basic operations. For example, the inverse operation of addition is subtraction, and the inverse operation of subtraction is addition, and so on.

Question 12

The result of each operation — goes by a different name. What are those?

Answer 12

• When you add two numbers together, you arrive at a sum.
• When you subtract, all that remains is a difference.
• When you multiply, you come up with a product.
• When you divide, you are left with a quotient.

Question 13

What is the order of operations?

Answer 13

Parentheses

Exponent

Multiplication & Division

Addition & Subtraction

Question 14

If you are dealing with a fraction, how do you suppose to treat the numerator and the denominator when solving?

Answer 14

Treat it as if it’s in parentheses, even if the parentheses aren’t written in the original state.

Question 15

How do you find the pattern in a sequence?

Answer 15

1. Identifying what operation was required to be used based on the sequence.
2. And always account for sequences that uses 2 operations (e.g., “add 1, subtract 1, add 2, subtract 2: 2,3,2,4)

Question 16

How can you find the average of a data set?

Answer 16

Find the mean, which can be expressed as mean = sum of the data/how many data there are.

Question 17

What is the median?

Answer 17

The median is the middle value in a set of ordered numbers. You can find it by putting your numbers in numerical order, from smallest to largest. in the data set 47, 56, 58 63, 100, the median is 58.

Question 18

What is the mode?

Answer 18

The mode is the value or values that occur most often in a list of numbers. If no numbers are repeated, there is no mode. but in the earlier data set with the test scores — 35, 35, and 50 — the mode is 35 because it appears most often.

Question 19

What is a fraction? Explain. Encode.

Answer 19

If a whole number is a pizza, a fraction is a slice of pizza. A fraction also illustrates the slice’s relationship to the whole pizza. For example, consider the fraction 3/5. if you accuser your cousin of eating 3 of the pizza when they come over for movie night, you are saying that the pizza is divided into five equal-sized slices — fifths — and your cousin ate three of those five slices.

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.

Question 20

What is the relationship of having common denominators and preparing to add and subtract fractions?

Answer 20

To add and subtract fractions, the fractions must have the same denominator (bottom number), which is called a common denominator. If the fractions do not have a common denominator, you have to find one.

Question 21

Why can you also express 3/5 as 6/10? Explain.

Answer 21

If you cut the pizza into 10 slices instead of 5 and your cousin eats 6 slices instead of 3, they have eaten exactly the same amount of pizza.

Question 22

What are the 2 methods that you can use in order to add or subtract fractions with different denominators?

Answer 22

1. Dividing the larger denominator by the smaller denominator method.
2. Multiplying the denominator method.

Question 23

How can you find the common denominators of a three or more fractions?

Answer 23

all denominators must be eligible to divide evenly into all new denominators.

e.g., the common denominator of ½ + ⅔ + 3/5 is 30

Question 24

How do you multiply fractions?

Answer 24

You just multiply the numerators and then multiply the denominators. For example: ½ x ¾ x 3/5 = 9/40

Question 25

A number that you can divide into both the numerator and the denominator is called…

e.g., 6/10 (simplified version: 3/5 when divided by 2).

Answer 25

a common factor

Question 26

How can you make this problem simpler to solve?

20/21 x 14/25 = 280/525 = 8/15

Answer 26

• 20/21 x 14/25 divide 20 and 25 by 5
• 4/21 x 14/5 divide 21 and 14 by 7
• 4/3 x 2/5 multiply
• 8/15

Question 27

How do you divide fractions?

Answer 27

Dividing a fraction by a number is the same as multiplying it by the multiplicative inverse (reciprocal) of that number.

FOR EXAMPLE:

⅓ ÷ 2 = 1/6 because it becomes ⅓ x ½ = 1/6

Question 28

How can you convert improper fractions to mixed numbers… and back again?

Answer 28

If you have a fraction with a numerator larger than or equal to its denominator, you have an improper fraction. For example, 7/3 is an improper fraction;

7 divided by 3 is equal to 2 with a remainder of 1 ||

the final answer is 2⅓

To convert it back so that you can multiply or divide…

1. Multiply the whole number by the denominator (bottom number) of the existing fraction to arrive at a new number. (2⅓ = 6/3)
2. Add that fraction to the original fraction to get the final answer. 6/3 + ⅓ = 7/3 = 2⅓

Question 29

How to change a fraction into a decimal?

Answer 29

To change the fraction into a decimal, you must divide the numerator by the denominator (3/5 = 0.6). Make sure that you round up your answers to the nearest hundreds.

To make a decimal a percent, move the decimal point two spaces to the right and add a percent sign. For example, 0.6 becomes 60%.

Question 30

What is the most important thing that you need to remember when adding or subtracting decimals?

Answer 30

keeping the decimal points in the same position in your answer.

Question 31

How do you multiply a decimal?

Answer 31

1. Multiply as though you were multiplying whole numbers, without the decimal points. (e.g., 3.77 x 2.8 =? would be 377 x 28 = 10,556)
2. Count and add the number of decimal places (to the right of the decimal point) in the numbers being multiplied. (e.g., 3.77 & 2.8 consists of 3 counts)
3. In the answer, move the decimal point back to the left by the number of places you counted in step 2. (e.g., 10,556 = 10.556)

Question 32

How do you divide decimals and whole numbers?

Answer 32

1. Move the decimal point over to the right until the decimal is a whole number, counting the number of decimal places (1.25 ÷ 4 into 125 ÷4).
2. Perform the division operation on the whole number (125 ÷ 4 = 31.25)
3. In your answer, move the decimal point to the left the number of places you moved it in step 1 (1.25 ÷ 4 = 0.3125).

Question 33

How do you divide decimals by decimals?

Answer 33

1. Make the divisor and the dividend into a whole number: Move the decimal point all the way to the right, counting the number of places you move it. (0.15 ÷ 0.25 into 15 ÷ 25).
2. Divide. (15 ÷ 25 = 0.60).

Question 34

To add, subtract, multiply, and divide percentages, you have to know how to convert percentages into a fraction or into a decimal. How?

Answer 34

• Remember, a percent is just hundredths, so 3% is 3/100 or 0.03.
• To convert a percent to a decimal, just drop the percent sign and move the decimal point two places to the left, adding zeros if needed.
• the decimal point always starts to the right of a whole number so 60 is the same thing 60.0. Moving the decimal point two spaces to the left leaves you with 0.6.

Question 35

What is a ratio?

Answer 35

def. A ratio shows a relationship between two things. For example, if Margaret invested in her tattoo parlor at 2:1 (or 2 to 1) ratio to her business partner, Julie, then Margaret put in $2 for every $1` that Julie put in. You can express a ration as a fraction, so it 2:1 is the same as 2/1.

Question 36

If the scale on a road map is 1 inch = 250 miles, how many inches would represent 1,250 miles?

Answer 36

x = 5, because…

1 : 250

1/250 = x/1,250

1/250(1,250) = x

1,250/250 = x

5 = x

Question 37

What is the difference between ratios and proportion in mathematics?

Answer 37

Proportion is a mathematical comparison between two ratios. When you see math (or real-world) problems that say things like “3 parts of vinegar, 1 part water,” you are dealing with a ratio ( and in this case, it’s 3:1). But when you compare two ratios (3 parts vinegar, 1 part water and 9 parts vinegar, 3 parts water) you are dealing with a proportion.

Question 38

What are inverse proportions?

Answer 38

Inverse proportions occur when one value increases and the other decreases. For example, more workers on a job reduce the amount of time necessary to complete a task.

Question 39

What is a rate?

Answer 39

A rate is a fixed quantity — a 5% interest rate, for example. It can mean the speed at which someone or something works (John reads at the rate of one page per minute), or it can mean an amount of money paid based on another amount (life insurance may be purchased at a rate of $1 per $100 of coverage). A rate is often a speed — something per a unit of time.

Question 40

What is the equation for simple interest?

Answer 40

Equation: I = Prt, where I represents the amount of interest, P is the principal (the initial amount invested), r is the interest rate written as a decimal, and t is the length of time in years the money is invested.

Question 41

What is THE EQUATION for distance?

Answer 41

Equation: d = rt, where d represents the distance traveled, r is the rate (speed) of travel, and t is the amount of time traveled.

Question 42

What is a scientific notation? Convert 5.79x10^-8 and convert 5.79x10⁸.

Answer 42

A scientific notation is a compact format for writing very large or very small numbers.

1. 579,000,000
2. 0.0000000579

Question 43

What are perfect squares?

Answer 43

Perfect squares are numbers with an exact square roots. For example, the square root of 25 is 5.

Question 44

What are irrational numbers?

Answer 44

Other whole numbers have square roots that are decimal that go on forever and have no pattern that repeats (nonrepeating, nonterminating decimals), so they are called irrational numbers. The square root of 30 is 5.4772255 with no end to the decimal places, so the square root of 30 is an irrational number.

Question 45

What is a root?

Answer 45

A root is a factor of a number that when cube (multiplied by itself three times), taken to the fourth power (multiplied by itself four times), and so on produces the original number.