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.


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