# GRE Arithmetic: Integers (Part 1 of 4) | Number Lines, Absolute Values, Addition, Subtraction

Arithmetic Review: Integers part one

The following series of videos will familiarize you with the mathematical skills and concepts

that are important to know, for the purpose of solving problems on the quantitative reasoning

section of the GRE revised General Test. The revised GRE Quantitative reasoning sections

are designed to measure your problem-solving ability, and focuses on basic concepts from

arithmetic, algebra, geometry, and data analysis. These videos will include many definitions,

properties, and examples keep in mind that this review is not intended to be all-inclusive

there may be some concepts on the test that are not explicitly presented in these videos.

Nevertheless you still need to acquaint yourself with the basic vocabulary and properties of

numbers. Initially the math concepts presented might be very simple but that doesn’t mean

they are not important. With that said let’s start with arithmetic and talk about integers.

We first need to remember the basics of number lines. Back in Algebra I and perhaps even

before that, you learned that a number line is formed when a numerical value is assigned

to each point on a line. For example the following line represents a number line and point A

is located at -1, likewise point B is located at positive 1. Notice that number lines are useful

to describe the location of a point relative to the origin which is usually assigned a

value of zero. Also notice that this line is broken into two regions or half’s. The

half on the right contains positive numbers and the half on the left contains negative

numbers. In general integers are whole numbers such as 1,2,3,4, and 5,… and so on together

with the negative integers such as -1,-2,-3,-4,-5 and so on along with 0 form the set of integers

and are represented by using set notation as follows: we enclose the numbers using curly

brackets like this recall that the ellipses mean that the numbers keep going forever and ever with

the implied pattern in other words the numbers keep going in both directions infinitely to

the left and infinitely to the right. Also notice that the set of integers are listed

consecutively, meaning that the integers are listed in order of increasing value without

any integers missing in between them. It turns out that positive integers are greater

than 0 and get bigger as you move away from zero for example 2 is greater than 1, likewise

the negative integers are less than 0 and they get smaller as they move away from zero

for example -2 is less than -1, and the number zero is neither positive or negative but remember

it is still considered an integer but does not have a particular sign, it is considered

sign neutral but an integer nonetheless. Any numbers between integers like one half,

one third, negative one forth are not considered integers they are called fractions. Remember

the set of integers do not contain fractional parts of a number. Moreover, fractions and

decimals cannot be listed consecutively like integers can. Fractions will be discussed

in a later video. Now that we know what integers are, let’s discuss the different types of

operations that can be used with integers. The 4 basic operations that can be applied

to integers are addition, subtraction, multiplication, and division. Before we talk about these operators lets talk about the absolute value of a number The absolute value of a number is equal to its distance away from 0 on the number line,

which means that the absolute value of any number is always positive whether the number

itself is positive or negative. The symbol for absolute value is a set of double lines. In essence the positive number of any pair of opposite non-zero numbers is called

the absolute value of each number in the pair. For example 1 and negative -1 form opposite

pairs one is a positive integer and the other a negative integer. The absolute value of

positive 1 is equal to 1 and the absolute value of negative 1 is equal to 1. In general

if a is a positive integer than the absolute value of a will be equal to a, if a is a negative

integer then the absolute value of a will be equal to negative a, and if a is zero then

the absolute value of 0 is equal to 0. Alright let’s move along and talk about, addition

and subtraction of integers. If we have two integers say a and b, then we can add them

in 5 distinct ways: if a and b are both positive then we add there absolute values and prefix

the positive sign for example 3 + 7=10, if a and b are both negative then we also add there absolute

values and prefix the negative sign for example:, -6 + (-2)=the sum of their absolute values (6+2) which is equal to 8 and then we prefix the negative sign if a is positive and b is negative and a has

a greater absolute value then b subtract b from a and prefix a positive sign to the result

for example: 8 + (-5) will be equal to 8 – 5 which is equal to 3. If a is positive and b is negative and b has a greater absolute value then a

subtract a from b and prefix a negative sign to the result for example: 4 + (-9) is equal to 9 – 4 which is equal to 5 and then we prefix the negative sign If a and be are opposites then there sum is equal to zero for example: 2 + (-2)=0 ok, In a nut shell, when adding or subtracting integers if the integers have the same sign, add their

absolute values and prefix their common sign. If the numbers have opposite signs, subtract

the lesser absolute value from the greater and prefix the sign of the integer having

the greater absolute value. Alright in our next video we will focus on

the concepts and terminology that are associated with the 3rd basic operator known as Multiplication.

If the Absolute value of any integer is always positive, why does it show in the video that if "a" is negative then it's absolute value is "-a"?

The absolute value of a number that is positive or negative is always positive. So in order to obtain a positive number from a positive integer we really don't need to do anything to the number since its all ready positive we leave it as it is. But, when we have a negative integer such as -5 the way we make it positive is by multiplying it by a negative, hence the absolute value of -5 is equal to -(-5) = 5 and that's why we have "-a" so that any number that is negative becomes positive.

Can you please upload the remaining GRE videos? i only see an artithmetic section.

u say that the bsloute value of negative integer will also be a postive number. then why sy absloute value of -a is –a.it should be a .

0:55 Number Lines

3:08 Operations

3:20 Absolute Value

4:13 Addition and Subtraction

Thank you