math for ACT
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| IMAGINARY NUMBERS | NUMBERS THAT INVOLVE SQUARE ROOTS OF NEGATIVE NUMBERS
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| EVEN NUMBER ARE DIVISIBLE BY | 2
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| prime numbers are divisible by | 1 and itself
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| composite number | divisible by more than just 1 and itself
eg..4,6,8,9,10,12,14,15...
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| squared means | numbers are multiplied by themselves.
eg..2x2=4 3x3=9 1,4,9,16,25,36...
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| cubed means | numbers are multiplied by themselves twice
2x2x=8 3x3x3=27
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| triangle formulas | perimeter=side+side+side
area=1/2bh
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| square formulas | perimeter=4s
area=sxs or s2
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| rectangle formulas | perimeter=2(b+h),or 2b+2h
Area=bh or lw
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| parallelogram formulas | perimeter = 2(l+w), or 2l +2w
Area =bh
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| Trapezoid formulas | perimeter = b1 + b2 + s1 + s2
Area = 1/2h(b1 + b2) or h(b1 + b2)
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2
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| circle formulas | circumference = 2pieR or pieD
area = pieR2
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| cube formulas | Volume = s~s~s=s3
Surface area = s~s~6
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| rectangular prism | Volume = l~w~h
Surface area = 2(lw) + 2(lh) +(wh)
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| 1/100 | .01 1%
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| 1/10 | .1 10%
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| 1/5 = 2/10 | .2 .20 20%
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| 3/10 | .3 .30 30%
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| 2/5 = 4/10 | .4 .40 40%
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| 1/2 = 5/10 = | .5 .50 50%
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| 3/5 = 6/10 = | .6 .60 60%
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| 7/10 = | .7 .70 70%
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| 4/5 = 8/10 = | .8 .80 80%
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| 9/10 = | .9 .90 90%
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| 1/4 = 25/100 = | .25 25%
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| 3/4 75/100 = | .75 75%
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| 1/3 = | .33 1/3 = 33 1/3%
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| 2/3 = | .66 2/3 = 66 2/3%
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| 1/8 = | .125 .12 1/2 = 12 1/2%
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| 3/8 = | .375 = .37 1/2 = 37 1/2%
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| 5/8 = | .625 = .62 1/2 = 62 1/2%
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| 7/8 = | .875 = .87 1/2 = 87 1/2%
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| 1/6 = | .16 2/3 = 16 2/3%
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| 5/6 = | .83 1/3 = 83 1/3%
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| 1 = | 1.00 = 100%
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| 2 = | 2.00 = 200%
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| 3 1/2 = | 3.5 = 3.50 = 350%
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| 3ft = | yard
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| 36 inches = | 1 yard
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| 1760 yards = | 1 mile
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| 5280 ft = | 1 mile
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| 5 1/2 yards = | 1 rod
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| 144 sq in = | 1 sq ft
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| 16 oz = | 1 lb
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| 2000 lbs = | 1 ton
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| 8 ounces | 1 cup
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| 2 cups | 1 pint
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| 2 pints | 1 quart
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| 4 quarts | 1 gallon
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| 8 dry quarts | 1 peck
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| 4 pecks | 1 bushel
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| 10 yrs | 1 decade
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| 100 yrs | 1 century
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| kilometer = | 1000 meters
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| hectometer (hm) | 100 meters
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| dekameter(dam) | 10 meters
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| 10 decimeters | 1 meter
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| 1000 millimeters(mm) | 1 meter
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| 1000 milliliters | 1 liter
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| 1000 liters | 1 kiloliter (kl)
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| terms of division | quotient divisor dividend ratio parts
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| vertical angles | formed by two intersecting lines,across from each other,always equal
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| adjacent angles | next to each other, share a common side and vertex
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| right angle | 90 degrees
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| straight angle, or line | measures 180 degrees
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| angle bisector | divides an angle into two equal angles
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| supplementary angles | two angles whose total is 180 degrees
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| complementary angles | two angles whose total is 90 degrees
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| what determines a line | two points
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| parallel lines | never meet; slopes are the same
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| perpendicular lines | meet at right angles; slopes are opposite reciprocals(ex: 1/3 and -3)
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| polygon | many sided (more that two) closed figure
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| regular polygon | a polygon with all sides and all angles equal
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| triangle | three sided polygon; interior is 180 degrees
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| equilateral | all sides are equal
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| isosceles triangle | two sides are equal
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| scalene triangle | all sides are different
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| in a triangle- | angles opposite equal sides are equal
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| in a triangle - an exterior angle | is equal to the sum of the remote two angles
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| median of a triangle | a line segment that connects the vertex and the midpoint of the opposite side
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| quadrilateral | four-sided polygon interior angles total 360 degrees
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| parallelogram | a quadrilateral with opposite sides parallel
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| rhombus | a parallelogram with equal sides
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| trapezoid | a quadrilateral with two parallel sides
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| pentagon | five sided polygon
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| hexagon | SIX sided polygon
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| radius of a circle | a line segment from the center of the circle to the circle itself
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| diameter of a circle | a line segment that starts and ends on the circle and goes through the center
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| chord | a line segment that starts and ends on the circle
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| arc | a part of the circle
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| to reduce a fraction | find the common denominator
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| to multiply fractions | line them up and multiply straight across
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| to divide fractions | invert the second and multiply
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| to change a fraction to a decimal | divide denominator into numerator
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| order of operation | p.e.m.a.s
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| every fraction implies | another fraction
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| a decimal is just another way to | express a fraction
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| in an average question you should think | total divided by #of things times average
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| 3x + 7 = 28 first step is | do the opposite of addition and subtract 7
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| 3x + 7 = 28 the second step | 3x = 28 get rid of the 3 do the opposite and divide both x=7
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| Act English, is (any form of the word be) IS THE SAME AS | =
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| Act English, of product times | x(multiply)
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| Act English, what a certain number | x,y,z(your favorite variable
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| Act English, what percent | x/100
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| Act English,more than, is added to the sum of increased by | add
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| one equation and two variables | can not be solved
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| working backwards on math questions | is often easier
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| when you solve an inequality, remember if you multiply or divide by a negative number | the sign flips
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| degrees in a circle | 360
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| degrees in a quadrilateral | 360
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| degrees in a line | 180
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| degrees in a perpendicular angle | 90
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| degrees in a triangle | 180
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| in geometry, because the problems are always drawn to scale | it will be possible to get very close approximation of the correct answers before you even do the problem
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| if you have no diagram | draw one
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| Transitive axiom | If a = b and b = c, then a = c.
1+3=4 and 4=2+2 then 1+3=2+2
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| cross multiplying notes | Cross multiplying can be used only when the format is two fractions separated by an equal sign.
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| reflexive | noting a relation in which each element is in relation to itself, as the relation “less than or equal to
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| axiom (a=a) | a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
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| Symmetric axiom | if a=b then b=a
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| solving equations |
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| cross multiplying in algebra | Be aware that cross multiplying is most effective only when the letter you are solving for is on the bottom of a fraction.
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| Addition/Subtraction Method | Combine equations to eliminate one variable. The equations may need to be multiplied by a common multiple first.
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| substitution method | Solve one equation for one variable and substitute that variable into other equations.
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| grafting method | Graph each equation on the same graph. The coordinates of the intersection are the solution.
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| to multiply Monomials | add the exponents of the same bases: x4(x3) = x7.
9882.html#ixzz0knPnlwRf
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| to divide monomials | subtract the exponent of the divisor from the exponent of the dividend of the same base: x8/x3 = x5.
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| add/subtract equations | Combine equations to eliminate one variable. The equations may need to be multiplied by a common multiple first.
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| add/subtract polynomials | add/subtract like terms only
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| multiply two polynomials | multiply each term in one polynomial by each term in the other polynomial.
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| the f.o.i.l method | first-outer-inner-last
is often used when multiply binomial
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| binomial | an expression that is a sum or difference of two terms, as 3x + 2y and x2 − 4x.
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| To divide a polynomial by a monomial | divide each term by the monomial
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| to divide a polynomial by another polynomial | make sure both are in descending order, then use long division (divide by first term, multiply, subtract, bring down).
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| distance is | rate x time
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| interest is | principal x rate x time
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| work accomplished | rate of work x time worked
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| How many irrational numbers are between 1 and 6 | there are an infinite number of irrational numbers between any two real numbers.
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| A number is divisible by 2 if its last digit is | 0,2,4,6,8
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| A number is divisible by 3 if the sum of its digits is divisible by 3. | 168 is divisible by 3 since the sum of its digits is 15 (1+6+8=15), and 15 is divisible by 3.
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| A number is divisible by 4 if the number formed by its last two digits is divisible by 4. | 316 is divisible by 4 since its last two digits are 16 and 16 is divisible by 4.
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| A number is divisible by 5 if its last digit is either 0 or 5. | 195
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| A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3. | 168 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.
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| A number is divisible by 8 if the number formed by its last three digits is divisible by 8. | 7,120 is divisible by 8 since its last three digits are 120 and 120 is divisible by 8.
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| A number is divisible by 9 if the sum of its digits is divisible by 9. | 549 is divisible by 9 since the sum of its digits is 18 (5+4+9=18), and 18 is divisible by 9.
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| any number raised to the 0 power is | 1 eg 1490 to the zero power = 1
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| any number raised sto the 1st power is itself | 81 =8 raised to the first power
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| a negative sign applied to a group | changes the sign of each term in the group
-(a+b)= -a + -b -(a + -b) = -a + b
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| Rules for subtracting integers: | # Change the problem to an addition problem.
* Subtracting a negative becomes adding a positive.
* Subtracting a positive becomes adding a negative.
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| Rules for adding integers: | neg+neg=neg
pos+pos=pos
poa+neg subtract keep the sign of the larger number
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| Rules for multiplying integers: | * A positive times a positive equals a positive.
* A negative times a negative equals a positive.
* A positive times a negative equals a negative.
* A negative times a positive equals a negative.
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| Rules for dividing integers: | # positive divided by a positive equals a positive.
# A negative divided by a negative equals a positive.
# A positive divided by a negative equals a negative.
# A negative divided by a positive equals a negative.
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| To cube a number | raise it to the third power
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| a root is | the opposite of an exponent spuare root of 81 is 9..16 is 4
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| order of operations | parentheses-exponents and roots-do all multiplication and division left to right -do what comes first do not do all multi than division do what comes first
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