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Algebra Rules Math0099
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The rules for my Math 0099 class
Terms in this set (56)
When multiplying 2 negative numbers the answer is a ......number
positive
When multiplying a positive and a negative number the answer is a ......number
negative
When numbers are the same (-)(-), the answer is a ......number
positive
When numbers are different, (-)(+), the answer is a ....number
negative
(-)(-), (+)(+), (-)÷(-), (+)÷(+) all equal a ....... number
positive
(-)(+),(-)(+),(-)÷(+), (+)÷(-) all equal a ...... number.
negative
If an exponent is even (-5²), the answer is a ...number.
positive 25
If an exponent is odd (-5³), the answer is a ....number.
negative -125
When a number is in parenthesis (a²)⁴ do you multiply or add the exponents?
Multiply the exponents: (a²)⁴= a⁸
Anything to the ⁰ (zero) power equals 1. T or F
True: 4⁰= 1
When a number is not in parenthesis a² x a³ do you multiply or add the exponents?
Add the exponents: a³ x a²= a⁵
When you multiply exponents do you add or subtract the exponents?
Add the exponents: a²÷b² x a⁴÷b³ = a⁶÷b⁵; you also keep your base and add exponents: t⁰ x t¹⁶ = t¹⁷
The formula for the area of a circle is
A=∏r²
When multiplying with exponential notation, if the bases are the same, keep the base and add the exponent. T or F?
T: a² x a³= a⁵
When dividing with exponential notation, if the bases are the same, keep the base and subtract the exponent of the denominator from the exponent of the numerator. T or F?
T: a⁹÷a⁴ =a⁹-a⁴= a⁵
1 as an exponent equals....
a¹ =a
0 as an exponent equals.....
a⁰=1
Negative integers as exponents
a-ⁿ=1/aⁿ, 1/a-ⁿ=aⁿ
Area of a rectangle
A=lw
.......consists of variables, constants, numerals, operation signs, and/or grouping symbols.
An algebraic expression
When we replace a variable with a number, we say that we are ....... for the variable.
substituting
When we replace all of the variables in an expression with numbers and carry out the operations in the expression, we are.....
evaluating the expression.
In algebra, we ........ problems to equations.
translate
"Add, added to, sum, total, plus, more than, increased by" are all words that translate to what operation symbol?
addition (+)
"Subtract, subtracted from, difference, minus, less than, decreased by, take away" are all words that translate to what operation symbol?
subtraction (-)
"Multiply, multiplied by, product, times, of "are all words that translate to what operation symbol?
multiplication (×)
"Divide, divided by, quotient" are all words that translate to what operation symbol?
division (÷)
The numbers used for counting are called..... numbers
the set of natural {1,2,3...}
The numbers used for counting and 0 are called.......numbers.
the set of whole numbers
For each natural number, there is a new number to the left of zero on the number line called.....
the set of integers {...,-5,-4,-3,-2,-1,0,1,2,3,4,5...} we have positive and negative integers!
Quotients of integers with nonzero divisors are called.... numbers
rational ⅔, -⅔,⁷/₁, 4, -3, 0, -.17
The set of numbers a/b, where a and b are integers and b is not equal to 0 (b≠0) is a called the set of ..... numbers
rational
To .... a number means to find and mark its point on the number line.
graph
Rules for adding numbers: Positive numbers add the same as arithmetic numbers. The answer is ......
positive
Rules for adding numbers: Negative numbers add absolute values. The answer is ....
negative -12 + (-7)= -19 add the absolute values:
|-12| + |-7|=12 +7 = 19. Make the answer negative: -19
If a number is negative, its absolute value is its....if a number is positive, its absolute value is ....
opposite; find the absolute value of |-7|: the distance of -7 from 0 is 7, so |-7| = 7; positive
The ..... of a number is its distance from zero on the number line.
absolute value |x| is the symbol
Rules for adding numbers: adding a + number and a - number. If the numbers have the same absolute value, the answer is.....
zero 1.5 +(-1.5)=0
Rules for adding numbers: adding a + number and a - number. If the numbers have different absolute values, subtract the smaller absolute value from the larger. Then, if the positive number has the greater absolute value the answer is....
positive -1.4 +8.5 =7.1
Rules for adding numbers: adding a + number and a - number. If the numbers have different absolute vales, subtract the smaller absolute value from the larger. Then, if the negative number has the greater absolute value the answer is....
negative -36 + 21=-15
Subtracting by adding the opposite: for any real numbers "a" and "b", a -b can be written....
a -b =a+ (-b)
think: "a" minus "b" is "a" plus the opposite of "b"
When multiplying more than 2 numbers we can choose order and grouping as we please. T or F?
True
The product of an even number of negative numbers is.......
positive: -5 x (-2) x (-3) x (-6) = 10 x 18=180
The product of an odd number of negative numbers is......
negative: (-3)(-5)(-2)(-3)(-6)= (-30)(18)= -540
Evaluate (-x)² and -x² when x=5
To find (-x)² we take the opposite and then square
(-x)²=(-5)²=(-5)(-5)=25. To find -x² we find the square and then take the opposite -x²= -(5)²=
-(25)=-25
The quotient of a÷b or a/b is that unique real number c for which a=b times c. T or F?
T
When two number like ½ and 2 are multiplied, the result is...... Such numbers are called.....of each other.
a positive number 1, reciprocals
The reciprocal of a positive number is also a ..... number, because the product of the two numbers must be the ......number....
positive, positive , 1
The reciprocal of a negative number is also a ...... number, because the product of the two numbers must be the ........number......
negative, positive, 1
Keep in mind that the opposite of a number is what we .... to the number to get zero.
add -3/8 and opposite number 3/8 = 0
Keep in mind that the reciprocal is what we ....... to the number to get 1.
multiply -3/8 and reciprocal -8/3=1
The reciprocal of a number has the .....sign as the number itself.
same: -3/8 and reciprocal -8/3=1
To divide, ...... by the reciprocal of the divisor.
multiply: -4 ÷3 is the same as -4 times ⅓
Caution: remember not to change the sign when taking a reciprocal
The opposite of a number "a" divided by the opposite of another number "b" is the same as the quotient of the 2 numbers a and b. Give an example
-a/-b= a/b or -5/+6 = +5/-6 or -(5/6)
The opposite of a number "a" divided by another number "b" is the same as the number "a" divided by the opposite of the number "b", and both are the same as the opposite of "a" divided by "b". Give an example
-a/+b= +a/-b= -(a/b) or +10/-3= -10/+3or -(10/3)
To subtract 2 numbers, add the 1st number to the ............of the 2nd number
opposite: -5.3-8.8= -5.3 + (-8.8)= -14.3
THIS SET IS OFTEN IN FOLDERS WITH...
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