Math 1 Flashcards
Real number
Any number on the number line including positive, negative, zero, fractions, decimals
Integers
All positive and negative WHOLE numbers, including zero
Commutative property
Switch order (addition and multiplication)
a+b=b+a
ab=ba
*can rewrite subtraction as addition of negative
7-4=7+(-4)=(-4)+7
Associative property
Grouping (addition and multiplication)
A+(b+c)=(a+b)+c
a(bc)=(ab)c
Distributive property
A(b+c)=ab +ac
A(b-c)=ab-ac
Multiplying by zero
Anything times zero equals zero
Zero product property
If product of two numbers is zero, one factor must be zero
If ab=0, then a=0 or b=0
Dividing number by itself
If a doesn’t equal 0, then a/a=1
(Negative) - (positive)
Or
(Negative) + (negative)
Factor out negative sign
(-46)-37 = -(46+37) = -83
(Small positive) - (bigger positive)
Or
(Small positive) + (big negative)
Factor out negative and reverse order of subtraction
23-64= -(64-23)= -41
Sign rules for multiplication/division
Same sign=positive
Different sign=negative
Absolute values
Gives the distance of the number from the origin
|x-5|= distance of x from +5
|x+3|= distance of x from -3
Order of operations
GEMDAS (grouping)
Always cancel before multiplying
Work from inside out with groups
Multiplying decimals
Count number of digits to right of decimal and multiply as whole numbers
6.25 x 0.048 ; 2+3=5 decimal places
625 x 48 = 30000 = 0.3
Decimal exponents
(0.3)^3=(0.03) x (0.03) x (0.03)
Then like multiplication rules: 6 places to the right of the decimal
3^3=27 ; .000027
Dividing decimals
Slide decimal for both numbers to the right until you have two whole numbers (or until it’s easier to solve)
0.56/0.0007=5600/7=800
Fractions to decimals
2/5
0.4
Fractions to decimals
3/5
0.6
Fractions to decimals
4/5
0.8
Fractions to decimals
5/6
.8333 …
Squaring multiple of 10
Square nonzero, then tack in two zeros at end
70^2 = 4900
Squaring number ending in 5
1) remove the 5, leaving remaining digit(s)
2) add one to remaining digit(s)
3) multiply numbers from first two steps
4) put product in front of 25
35^2
3+1=4
3*4=12
35^2=1225
If we know value of n^2, (if n is multiple of 5,10), we can get next square up, (n+1)^2, by adding n and (n+1)
41^2 = 40^2 +40 + 41
X
Dividing by 5
Double N and divid by 10
235/5 = 470/10 = 47
Equivalent fractions
Fractions with equal numerical value even tho they have different numerators and denominators
Fraction in lowest terms
Equivalent fraction with lowest possible numerator and denominator (simplifying)
Undefined fraction
Denominator equals zero
Improper fraction
Numerator > denominator
5/3
Mixed numeral
Integer part + fraction part
Complex fraction
Large fraction with smaller fractions within its numerator, denominator
Reciprocal fraction
Flipped over fraction
1/(3/7) = 7/3
Adding fractions
Get common denominator
Multiplying fractions
Multiply across in numerator and denominators
Cancel first
Dividing by fractions
Multiply by its reciprocal
Proportions
Equation in the form
Fraction=fraction
Fraction word problems
"Is" = equals "Of" = multiply
“What is 3/5 of $400?”
3/5400=3/5400/1=3/1*80/1=$240
Multiplier
Decimal form of a percent
“What is 80% if 200?”
(0.80)*200=160
“56 is what percent of 800?”
56=800x
X=56/800=7/100=0.07=7%
Percent increase
“Y increase by 30%” or “X is 39% greater than Y”
If Y increases by 30%, the whole original part of Y is still there plus 30% more
Multiplier for 30% increase: 1+0.3=1.3
Percent decrease
“Y decreased by 30%” or “X is 30% less than Y”
If Y decreases by 30%, the whole original part of Y is still there except for 30% missing
Multiplier for 30% decrease: 1-0.3=0.7
Attention: percent increase/decrease question phrasing
The price of an item increases from $200 to $800. What is the percent increase?
Not 400 but 300%! 4 is only multiplier, not final percent INCREASE!
Multiple percent increases/decreases
Multiply multipliers together to get multiplier of percent increase/decrease
It increases by 20% and then decreased by 50% and finally increased by 40%. Percent change is:
(1.2)(0.5)(1.4)=0.84, 16% decrease
Simple interest
Interest remains same amount based on principle every term
Bob receives $50 interest on $1000 every month. Always $50.
Prime
A number with only two factors : 1 and itself
2,3,5,7,11 …
Composite number
Has more than two factors (not prime)
Prime numbers
Only two factors, 1 and itself
MEMORIZE
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
Undefined fraction
Denominator = 0
