Transcript File

LEARNING GOAL:
By the end of this lesson, I
will be able to write and solve
Algebraic equations.
Writing Equations –
Odd & Even Integers
Consecutive Integer Problems
In order to work with a
“consecutive integer” problems,
we need to start by
understanding the terminology:
Consecutive
Consecutive means: “In a
row” or “In order.”
– ALGEBRA I –
Unit 1 – Section 2
Consecutive Integer Problems
Integer
An integer is: a nice, round,
positive/negative number.
– ALGEBRA I –
Unit 1 – Section 2
Consecutive Integer Problems
Let’s go
through
some
examples.
The key thing to remember is
that your answers will be
consecutive integers. In other
words, the numbers you get
should be “nice” (a.k.a. no
fractions or decimals) and they
should be in a row.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is 51.
• The first thing to note is that we are dealing with
consecutive integers.
• An example (that is not necessarily the solution) of
consecutive integers could be:
20 21 22
+1
Notice that to get from the first number in the list
to the second, we need to add 1.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is 51.
20 21 22
+1
+2
To get from the first number in the list to the third,
we need to add 2.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is 51.
• Instead of using numbers, we need to switch to
variables.
20 21 22
+1
+1
+2
+2
N N+1 N+2
• Note that we follow the same “addition” procedure.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is 51.
• Now to start the problem, we begin by writing the
expressions for the THREE integers:
N
N+1
N+2
• Since we are looking for the sum, the equation is:
N + (N + 1) + (N + 2) = 51
Example Problems
Consecutive EVEN Integer Problem
The product of two consecutive
EVEN integers is 120.
• The first thing to note is that we are dealing with
consecutive EVEN integers.
• An example (that is not necessarily the solution) of
consecutive integers could be:
20 22 24
+2
Notice that to get from the first number in the list
to the second, we need to add 2.
Example Problems
Consecutive EVEN Integer Problem
The product of two consecutive
EVEN integers is 120.
20 22 24
+2
+4
To get from the first number in the list to the third,
we need to add 4.
Example Problems
Consecutive EVEN Integer Problem
The product of two consecutive
EVEN integers is 120.
• Instead of using numbers, we need to switch to
variables.
20 22
+2
+2
N N+2
• Note that we follow the same “addition” procedure.
Example Problems
Consecutive EVEN Integer Problem
The product of two consecutive
EVEN integers is 120.
• Now to start the problem, we begin by writing the
expressions for the TWO integers:
N
N+2
• Since we are looking for the product, the equation is:
N (N + 2) = 120
Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD
integers is 57.
• The first thing to note is that we are dealing with
consecutive ODD integers.
• An example (that is not necessarily the solution) of
consecutive integers could be:
21 23 25
+2
Notice that to get from the first number in the list
to the second, we need to add 2.
Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD
integers is 57.
21 23 25
+2
+4
To get from the first number in the list to the third,
we need to add 4.
Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD
integers is 57.
• Instead of using numbers, we need to switch to
variables.
21 23 25
+2
+2
+4
+4
N N+2 N+4
• Note that we follow the same “addition” procedure.
Example Problems
Consecutive ODD Integer Problem
The sum of three consecutive ODD
integers is 57.
• Now to start the problem, we begin by writing the
expressions for the THREE integers:
N
N+2
N+4
• Since we are looking for the sum, the equation is:
N + (N + 2) + (N + 4) = 57
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is equal to 3 times the greatest integer.
• The first thing to note is that we are dealing with
consecutive integers.
• An example (that is not necessarily the solution) of
consecutive integers could be:
20 21 22
+1
Notice that to get from the first number in the list
to the second, we need to add 1.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is equal to 3 times the greatest integer.
20 21 22
+1
+2
To get from the first number in the list to the third,
we need to add 2.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is equal to 3 times the greatest integer.
• Instead of using numbers, we need to switch to
variables.
20 21 22
+1
+1
+2
+2
N N+1 N+2
• Note that we follow the same “addition” procedure.
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is equal to 3 times the greatest integer.
• Note that we need to find three times the greatest
integer.
+1
+2
N N+1 N+2
• N + 2 is the greatest of these three integers.
• 3 times N + 2 is represented as
3(N +2)
or
3•(N + 2)
• The parentheses help us remember that we are using
the distributive property 3•N + 3•2
Example Problems
Consecutive Integer Problem
The sum of three consecutive integers
is equal to 3 times the greatest integer.
• Now we have to put the whole equation together.
N + (N + 1) + (N + 2) = 3(N + 2)
The sum of three
consecutive integers
is
Three times the
greatest integer