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Praxis Core Math (FULL)
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Terms in this set (96)
Proper Fraction
A fraction that represents a quantity that is less than 1
Improper Fraction
A fraction that represents a quantity that is more than one
How to Raise a Fraction
Multiply both terms by the same number
How to Reduce a Fraction
Divide both terms by the same number
Common Denominator & How to Find it
The numbers below the fraction bar are the same. To find it is to list the multiples of of both denominators
Ex. 5/6 + 1/4
Multiples of 6: 6,12,18
Multiples of 4: 4,8,12,16
12 is the common denominator
How to Multiply fractions
multiply numerators then the denominators. Reduce to lowest terms if necessary. If mixed number turn to improper fraction
How to Divide Fractions
Invert the divisor (the fraction you are dividing by) by switching its numerator and the denominator. Then multiply the fractions.
Ex. 8 Devide at by 1/2.
8 (/) 1/2 = 8/1 (/) 1/2
8/1 x 2/1 = 16/1 = 16
Part-to-part ration example
Rate of blue compared to rate of red marbles in a bag
Part-to-whole ration example
rate of blue marbles in a bag of 100
Proportion
An equation thta shows that two ratios are equal. In other words, if you multiplly across the equal sign, the products are equal.
Ex. 2 cups of water to every two scoops of drink mix. How many cups of water will you need for 12 scoops of drink mix?
cups/scoops = 3/2 = 12/8
3 x 8 = 24
2 x 12 = 24
Rate
Compares the number of units of one item to one unit of another item.
Equation for solving a percent
percent = part/whole OR part = percent x whole
Ex. What is 2% of 900?
x = 2% x 900
x= 18
Probability
The numerical representation of the likelihood of an event or events occurring
Equation for probability
Probability (event) = # of favorable outcomes possible/ # of total possible outcomes
Multiples
A number that is divisible by another number with no remainder is a multiple of that integer
Factors of a number
positive integers that evenly divide into that number
Divisibility test of 3
If sum of its digits are divisible by three
ex. 4317
4 + 3 + 1 +7 = 15
15 is divisible by 3
Divisibility test of 4
if last two digits are divisible by 4
ex. 1748
48 is divisible by 4
Divisibility test of 6
If it is divisible by both 2 and 3
ex. 4326
Divisible by two
4 + 3 + 2 + 6 = 15
Divisible by three
Divisible by six
Divisibility test of 9
If the sum of its digits is divisible by 9
Ex. 22428
2 + 2 + 4 + 2 + 8 = 18
18 is divisible by 9
Origin
The point in which two axes intersect on a plane
X-axis horizontal or vertical?
Horizontal
Y-axis horizontal or vertical?
Vertical
Evaluating an expression
Finding its value. To do this, substitute a given number for each variable.
Consecutive Integers
numbers that are evenly spaced and follow in the counting order
ex. 1, 2, 3.
Finding a consecutive integer
Ex. the sum of three consecutive integers is 105. What is the greatest of the three numbers?
x + (x+1) + (x+2) = 105
3x + 3 = 105
3x = 102
x = 34
Steps to interpreting a graph
1. Read the Labels
2. Analyze the Data
3. Use the Data
To add without a number line
If numbers have like signs, ad the numbers to keep the signs
If numbers have unlike signs, find the positive difference between the two numbers and the us the sign of the larger number
What is 8^1?
8
What is 6^0?
1
What is 4^-2?
4^-2= 1/4^2 = 1/4x4 = 1/16
1/16
Perimeter
The distance around the figure
Perimeter of a square
Perimeter = 4 x side OR p=4s
Perimeter of a rectangle
Perimeter= 2 x length + 2 x width OR p=2l=2w
Perimeter of a triangle
Perimeter= side 1 + side 2 + side 3 OR p=a+b+c
Area
The space inside of a figure
Area of a square
Area=side^2 OR a=s^2
Area of a Rectangle
Area= length x width OR a=lw
Area of a parallelogram
area= base x height OR a=bh
Area of a triangle
area= 1/2 x base x height OR a=1/2bh
Area of a trapezoid
area=1/2(base one + base 2) x height OR a=1/2(b1+b2)h
What does it mean when it says "Circumference of a circle"?
It is its perimeter or the distance around the circle
What is the diameter of the circle?
A line segment with endpoints on the circle that passes through the center of the circle. It goes right through the middle from one end to the other
What is the radius of a circle?
A line segment that connects the center of the circle to a point on the circle. It is one half of the diameter.
Formula for circumference of a circle
Circumference = (pie) x diameter or C=(pie)d
How is the radius of the circle connected to the circumference of a circle?
to find the racius you need to multiply pie to the diameter. Since the radius is half of the diameter, you can find the circumference of the circle without having the diameter by
c= 2(pie)r
Formula for area of a circle
A = (pie) x radius^2 or A=(pie)r^2
Volume
The measure of space inside of a three-dimensional object
Formula for volume of a rectangular solid
volume = length x width x height OR v=lwh
Formula for volume of a cube
volume = edge^3 OR v=e^3
Formula for volume of a cylinder
Volume = (pie) x radius^3 x height OR v=(pie)r^2h
Right Angle
Angle that = 90
Acute Angle
Angle that is LESS than 90
Obtuse Angle
Angle that is GREATER than 90 but LESS than 180
Reflex Angle
Angle that is GREATER than 180 but LESS than 360
Complementary
When the sume of two angles is 90
Supplimentary
When the sum of two angles is 180
Vertical angles
Angles that have the same measures after two lines intersect. Each time they intersect, two pairs of vertical angles are created
Adjacent angles
Angles that share a common ray.
Transversal
A line that intersects two or more other lines
Corresponding Angles
An angle that matches another angle in the same position on the transversal line
Alternate exterior angles
Are equal in measure. They are on opposite sides of the transversal and are on the outside of the parallel lines
Alternate interior angles
Are equal in measure. They are on opposite sides of the transveral are are on the inside of the parallel lines ( 5 and 6)
Equilateral Trangle
All sides are equal in length. The angles are all equal in length as well.
Isosceles Triangle
Exactly two sides are equal in length.
The two angles opposite these sides are equal.
Scalene Triangle
No sides are Equal in length, and now angles are equal
Right Triangle
One angle in a triangle is equal to 90
Acute triangle
ALL angles measure less than 90
Obtuse Triangle
One angel is greater than 90
Rules in determining similarity
1. If two angle measures in the first triangle are equal to two angle measures in the second triangle, the triangles are similar
2. If all corresponding sides have the same ration, the triangles are similar
Quatrilateral
A closed shape with four sides
A rectangle
A four-sided quadrilateral with four right angles
A Square
A four-sided quadrilateral with four right angles AND each side is the same length
A Parallelogram
A four-sided figure whose opposite sides are parallel and the same length. The opposite angles are equal in measure.
A Trapezoid
A four sided figure with only two parallel sides
How many inches are in a foot?
12
How many feet is in a yard?
3
How many ounces are in a cup?
8
How many cups are in a pint?
2
How many pints are in a quart?
2
How many quarts are in a gallon?
4
How many ounces in a pound?
16
How many pounds are in a ton?
2,000
Kilo
Thousand
ex. 1 Kilometers = 1000 meters
Hecto
Hundred
Ex. 1 hectometers= 100 meters
Deca
Ten
Ex. 1 Decameter= 10 meters
Deci
One-tenth (1/10)
Ex. 1 decimeter= .1 meter
Centi
One-hundredth (1/100)
ex. 1 centimeter = .01 meter
Milli
One-Thousandth
ex. 1 millimeter= .001 meters
English system of measurement: How to change a larger unit to a smaller one
You need to multiply.
ex. A picture frame is 3 feet 8 inches long What is the length of the frame in inches?
3 ft x 12 = 36 in.
36 in + 8 in = 44 in.
44 inches
English system of measurement: How to change a smaller unit to a larger one
Divide using the appropriate measurement equivalency.
ex. A package weighs 84 ounces. What is the weight of the package in pounds?
84 / 16
the remainder is 4 (which represents four ounces left over after the conversion.)
package weighs 5 lbs. 4 oz.
English system of Measurement: Multiply
Multiply the units of a meausre seperately then simplify the result.
ex. Tony has five lengths of plastic pipe, each measureing 6 feet, 10 inches. What is the combined legnth of the five pieces of pipe?
6 ft 10 in x 5
30ft x 50 in
30ft + 4ft 2 in
34 ft 2 in
Metric System: How to change larger unit to smaller unit
move decimal to the left
ex. How many grams are equal to 6,400 milligrams?
6.4g
Metric System: How to change smaller unit to larger unit
Move decimal to the right
ex. How many millimeters are equal to 3 centimeters?
30 millimeters
Metric System: Divide
use rules for multiplying and dividing decimals
ex. At a food-processing plan, a storage tank holds 92.4 liters of a fruit drink. It takes three hours for a machine to empty the tank into small containers. How many liters of fruit drink are processed per hour?
Divide 92.4 liters by 3
the machine processes 30.8 liters per hour.
Metric System: Multiply
Use rules for multiplying and dividing decimals
ex. Alex is a buyer at Rugs plus. he plans to order 25 acrylic rugs to sell in the store. The shipping weight for each rug is 7.8 kilograms. What is the shipping weight in kilograms of the store order?
Multiply the weight of one rug (7.8 g) by 25
the weight of the 25 rugs is 195 kilograms.
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