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Praxis II-Multiple Subjects-Math section
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Terms in this set (40)
communicative property
The product is the same regardless of the order of factors.
Example: 2x5=5x2
associative property
The product is the same regardless of grouping.
Example: (2x5)x3=2x(5x3)
distributive property
Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Example: 2x(3+4)=(2x3)+(2x4)=14
zero property
The sum of a number and 0 is that number. In multiplication, the product of a number and 0 is 0.
Example: 3+0=3 and 3x0=0
integers
The set of positive and negative numbers, including zero.Integers do not include fractions (1/3), decimals (0.56), or mixed numbers (7 3/4).
prime number
A whole number great than 1 that has only two factors, itself and 1; a number that can be divided evenly only by 1 and itself.
Example: 3,7,11
composite numbers
A whole number greater than 1 that has more than two different factors. In other words, any number that is not a prime number.
Example: Composite number 8 has the factors of 1,2,4,8
even numbers
any number that can be divided by 2 without leaving a remainder.
Example: 2,4,6,8,10
odd numbers
any number that cannot be divided evenly by 2.
Example: 3,5,7,9,etc.
rational numbers
the set of whole numbers, integers, decimals, and fractions.
Example: 45.6 can be written as 456/10
irrational number
numbers that are not rational
Example: Pi=3.141592653
real numbers
the set of all rational and irrational numbers
Example: 1,2,3,4,5 etc.
factors
numbers that are multiplied together to obtain a product
Example: 2*3=6
2 and 3 are factors
common factor
a number that divides exactly into two or more other numbers
Example:
Factors of 12 are 1,2,3,4,6, and 12
Factors of 15 are 1,3,5,15
-Common factors of 12 & 15 are 1 & 3
prime factor
also a prime number
-The prime factors of 12 are 1,2,and 3
-The prime factors of 15 are 1,3,and 5
fraction
a way to compare equal parts with a whole
Example: 5/8 shows that there are 5 equal parts out of 8 equal parts
numerator
top number of a fraction
denominator
bottom number of a fraction
decimal
a number that uses a decimal point to show tenths, hundredths, thousandths, and so on
Example: 1.234
PEMDAS order of operations
Please (Parenthesis) Excuse (Exponents) My (Multiplication) Dear (Division) Aunt (Addition) Sally (Subtraction)
cardinal numbers
numbers we use for counting
Example: 1,2,3,4,5,6,7,8
ordinal numbers
used to show position
Example: 1st, 2nd, 3rd, 4th, etc.
least common denominator
the lowest multiple of one or more denominators of a fraction
greatest common factor
the largest number that is a factor of two or more numbers
Example:
GCF- 15: 1,3,5,15
35: 1,5,7, and 35
GCF=5
least common multiple
the smallest number that is a multiple of two or more numbers
Example:
LCM- 3:(1)3, (2)6, (3)9, (4)12, (5)15
5: (1)5, (2)10, (3)15, (4)20
LCM=15
equivalent fractions
two fractions that have the same value but are expressed differently
Example: 1/5=20/100=2/10=4/20 (2x2=4) (10x2=20)
simplifying a fraction
the numerator and denominator of a fraction are reduced to the smallest possible integers
Example: 4/8 simplified (4/4=1) (8/4=2) = 1/2
problem solving strategies
1.) use manipulatives or act out the problem
2.) draw a picture
3.) look for a pattern
4.) guess and check
5.) use logical reasoning
6.) make an organized list
7.) make a table
8.) solve a simpler problem
9.) work backward
decimals are fractions...
that are based on a whole of 100 instead of a whole of 1
Example: one whole is equal to 100%
("percent" means "for every hundred")
A fraction expressed as a percent
use formula %=100* (numerator/denominator)
Example: 3/5 expressed as a percent would calculate as %=100*3/5=300/5=60
3/5=60%
express a percents as a common fraction
divide the percent number by 100 and reduce to lowest terms
Example: 96%=96/100
=24/25
convert decimals to fractions
remember that percent means hundredths
Example: 0.23=23%
5.34=534%
0.007=0.7%
700%=7.0
86%=0.86
find the percent of a number
percent must first be changed to a decimal number. 30% becomes 0.3 is multiplied by the number in question
Example: find 30% of(multiply) 33
Step 1: 0.3x33=9.9
so 9.9 is 30% of 33
average
a single value used to represent a collection of data
mean
formula=sum of values/number of values
median
the middle value of a distribution that is arranged in size order
median=1/2 (n+1)
n=# of values
If there is an even # of values then add the who middle numbers & divide by 2
mode
the value(s) that occur the most often in a distribution
Example: 21,23,25,27,27,27,28,30
mode=27
absolute value
a numbers distance from zero
Example: -3 & +3 have an absolute value of 3 (both are 3 spaces away from 0)
subtracting a positive
subtract the absolute value and give the sum the sign of the larger addend
Example: +7-(+3)=7-3=4
or -5-(+9)
exponent
the superscript number placed next to another number at the top right to indicate how many times the number is multiplied by itself
Example: 3^3=3x3x3=27
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