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January 4, 2016
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Vocabulary
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Vocabulary
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Real Numbers- nearly any number you can think of
(whole number, rational number, irrational numbers)
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Rational Numbers- a number that can be written as a
fraction
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Integers- all positive and negative numbers (no
fractions!)
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Whole Numbers- all counting numbers including 0 (no
fractions)
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Natural Numbers- counting numbers or whole
number
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Irrational Numbers- a number that cannot be made
by dividing two numbers (cannot be written as a
fraction)
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Consecutive Integers
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Consecutive Integers -integers that follow each other in order
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Example: 1, 2, 3, 4, 5, 6, 7, ...
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Represented Algebraically: x, x+1, x+2, x+3
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x is always the first integers
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x+1 represents the next integer because they are consecutive, therefore
each is 1 more then the previous
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sum: add the consecutive integers (example: (x)+(x+1)=15)
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difference: subtract the consecutive integers (example: (x)-(x+1)= 13)
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must use an algebraic expression to solve these types od problems
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Consecutive Even Integers
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Consecutive Even Integers –even integers that follow each other in order
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Example: 2, 4, 6, 8, ...
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Represented Algebraically: x, x+2, x+4, x+6
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x is always the first integers
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x+2 represents the next even integer because by adding 2 we are
eliminating the odd numbers
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sum: add the consecutive even integers (example: (x)+(x+2)=16)
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difference: subtract the consecutive even integers (example: (x)-(x+2)= 14)
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must use an algebraic expression to solve these types od problems
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Consecutive Odd Integers
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Consecutive Odd Integers –even integers that follow each other in order
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Example: 3, 5, 7, 9, ...
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Represented Algebraically: x, x+2, x+4, x+6
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x is always the first integers

x+2 represents the next odd integer because by adding 2 we are eliminating
the even numbers
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sum: add the consecutive odd integers (example: (x)+(x+2)=16)
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difference: subtract the consecutive odd integers (example: (x)-(x+2)= 14)
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must use an algebraic expression to solve these types od problems
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Practice Problems
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1. The sum of four consecutive integers is -42. What are the
integers?
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2. The sum of four consecutive even integers is -100. What are
the integers?
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3. Find three consecutive odd integers whose sum is 105.
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4. The sum of three consecutive odd integers is 40 more than the
smallest. What are the integers?
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5. The greater of two consecutive even integers is six less than
twice the smaller.
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6. The least of three consecutive odd integers is 2 more than half
the largest. What are the integers?
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Transforming Equations
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“In terms of”- what equation equals
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Concept: Get a specific variable on one side and all other
variables on the other
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Follow the same rules as regular algebra (think
opposites)
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Sample
y = 5x + 7
-7
-7
y-7= 5x
5
5
y-7 = x
5
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Sample
ab-d = c
+d
+d
ab = c+d
a
a
B = c+d
a
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Practice
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dx=c
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A= P + Prt
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c = d/ g
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S=C + rC
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z-a = y