Download Things Ninth Graders Need to Know Vocabulary Terms Terms are

Things Ninth Graders Need to Know
Vocabulary
1. Terms
Terms are expressions that are separated by addition, or things that are added.
In the expression
3+4+5
In the expression
5 x 2  3x  4
3,4 and 5 are terms
5 x 2 , 3x and 4 are terms
2. Factors
Factors are expressions that are separated by multiplication, or things that are multiplied.
In the expression
In the expression
3(4)(5) 3, 4 and 5 are factors.
5xy 5, x and y are factors
3. Coefficients
Factors that are also numbers are called coefficients.
In the expression
5xy
5 is not only a factor, it is a coefficient.
4. Like Terms
Terms whose only difference is the coefficient.
Algebraic Operations
5. Subtraction and division are not algebraic operations.
a  b means a  b
3  5 or
subtraction means add the oppsite
3
1
both mean 3  
5
5
division means muliply by the reciprocal
Properties that make the game go
6. Commutative (The order of the factors or terms around an algebraic operation change)
57  75
5x2  x2  5
7. Associative (The order of consecutive additions or multiplications changes)
5  7  3 can be 12+3 or 5+10
(a  b)  c  a  (b  c)
5  7  3 can be 35  3 or 5  21
(a  b)  c  a  (b  c)
8. Distributive (Multiply through or factor out)
This is the property that allows us to add “like terms”.
a  b  c   ab  ac
7 105  7 100  5   7 100  7  5  700  35  735
2 x  8  2( x  8) The expression is factored.
5 x  6 x  x(5  6)  x 11  11x This why you can add like terms.
Exponents
9. Exponents that are natural numbers count factors.
x5 means x  x  x  x  x the factor x is written 5 times.
10. When multiplying add the exponents.
x3 x4 means
 x  x  x  x  x  x  x 
or x7
11. When there is a power (exponent) on a power, multiply the exponents.
x 
4 3
means x 4  x 4  x 4 or x12
12. Any number raised to the zero power is 1.
53  50  53 so 50 must be 1
13. Any time you multiply two numbers and get 1 the numbers are reciprocals.
x n and x  n are reciprocals
53  53  50 and 50  1 so 53 and 53 must be reciprocals
1
1
3
3

5
and
5

53
53
14. Roots and fractional exponents.
3
125  5 because 53  125
3
x3  x because x3  x3
1
3 3
5 
n
1
3
 5  5 so 125  5 and 125  125
1
xx
3
1
3
1
n
Lines
15. Slope
rise
run
y
Slope 
x
y y
Slope  2 1
x2  x1
Slope 
16. Equations
y  b  mx (b is the y-intercept and m is the slope)
y  y1  m( x  x1 ) (  x1 , y1  is any point on the line)
Variation
17. Direct variation
Whatever multiplier is used on x is used on y i.e. if x is multiplied by 3.2 so is y.
The ratio is constant.
y
 K or y  Kx
x
18. Inverse Variation
When a multiplier is used on x , y is multiplied by the reciprocal i.e. if x is multiplied by 5, y is
multiplied by 1/5. (divided by 5)
The product is constant.
xy  K or y 
K
x