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.