Download Area

Creating Equivalent
Fractions
1. Multiply or divide the
numerator and the denominator by
the same number.
Add/ Subtract Fractions
Rule: To add/subtract fractions,
they must have the same
denominator.
1/2 + 1/3 = ?
1. Create equivalent fractions
that have a common
denominator
2. Add the numerators
together and the denominator
stays the same.
3. Simplify the fraction.
Multiplying Fractions
2 1/2 x 4/7 = ?
1. Convert any mixed numbers
into improper fractions
(2 1/2 = 5/2)
2. Multiply the numerators,
then multiply the denominators
(5 x 4 = 20) (2 x 7 = 14)
3. Simplify. 20/14 = 1 6/14
1 6/14 = 1 3/7
Convert Fractions to Percents
1/9  .111  11.1%
1. Turn the fraction into a decimal.
2. Turn the decimal into a percent.
Convert Percents to Fractions
15% = 15/100 6% = 6/100
Percent just means “out of 100,” so
you simply make your percent the
numerator and your denominator
is 100.
Classifying Numbers
factor-a number that can be
multiplied to get another number.
1, 3, 5, and 15 are factors of 15.
multiple-a counting number of a
certain number
multiples of 15 are 15, 30, 45, 60…
prime-a number that has only 2
factors, 1 and itself.
2-1,2 3-1,3 5-1,5 7-1,7 11-1,11
composite-a number that has more
than 2 factors
4-1,2,4 6-1,2,3,6 12-1,2,3,4,6,12
Create Equivalent Fractions
w/Common Denominators
2/5 and 1/6
1. Multiply the numerator and
denominator of each fraction by
the other fractions denominator
Adding Mixed Numbers
4 1/2 + 3 3/5 =?
1. Add the whole numbers
together. 4 + 3 = 7
2. Create common denominators
for the fractional parts and add
those together.
1/2 5/10
2/5  6/10
5/10 + 6/10 = 11/10
3. Put the whole number part and
fractional parts together
4. Simplify.
4 1/2 + 3 2/5 = 7 11/10  8 1/10
Dividing Fractions
3/4  1/5 = ?
1. Flip the numerator and the
denominator of the fraction
after the division sign,
(1/5  5/1)
2. Turn the division sign into
a multiplication sign.
3/4 x 5/1 = 15/4
3. Simplify your answer.
15/4 = 3 3/4
Adding Positives and Negatives
-7 + 4 = ?
1. Ask yourself if there are
more positives or more
negatives. Whichever has
more, that will be the sign of
your answer. (more –‘s)
2. Ask yourself how many
more positives or negatives
there are and that is your
numeral (3 more)
-7 + 4= -3
Exponents
4^3 = “four to the third
power” or “four cubed”
4^3= 4 x 4 x 4
4^3 = 64
6^2 = “six to the second
power” or “six squared”
6^2 = 6 x 6
6^2 = 36
Converting Mixed Numbers to
Improper Fractions
2 1/5  11/5
1. Multiply the whole number
times the denominator(2 x 5= 10).
Then add the numerator
(10 + 1 = 11). This becomes your
new numerator (11).
2. Your denominator stays the
same (5). 2 1/5  11/5
4 1/3  13/3
1 1/2  3/2
9 5/6  59/6
Subtracting Mixed Numbers
3 1/2 – 1 4/5 =?
1. Identify if you have to trade (If
the first fractional part is less than
the second fractional part, then you
have to trade) 1/2 < 2/5, so we
need to trade. 3 1/2  2 3/2.
2. Subtract the wholes. 3 – 2 = 1
3. Create common denominators for
the fractional part and subtract.
3/2  15/10 4/5  8/10
15/10 – 8/10 = 7/10
4. Simplify.
3 1/2 – 1 4/5 = 1 7/10
Convert Fractions to
Decimals
1, Make an equivalent fraction
with either 10 or 100 as the
denominator.
2.Memorize common fractions and
their decimal conversions.
Ex: ¼ = .25, 2/3 = .67 3/5 = .6
3. Divide the numerator by the
denominator
Subtracting Positives and
Negatives
1. Change the “minus” sign to
an addition sign.
2. Take the opposite of the
number after the addition
sign.
3. Solve your new addition
problem.
-7 – 8 = ?  -7 + -8 = -15
5 – (-8) = ?  5 + (+8) = 13
6 - 9 = ?  6 + -9 = -3
Prime Factorization
Writing a number as a product of
only prime numbers, usually using
a factor tree.
60
Converting Improper
Fractions to Mixed Numbers
11/4  2 3/4
1. How many times does the
denominator go into the
numerator? 4 goes into 11, 2
times. That is the whole number
(2).
2. How much is left over? 4 goes
into 11, 2 times, with 3 left over. 3
is the numerator. The
denominator stays the same.
17/3  6 1/3
9/5  1 4/5
Simplifying Fractions
8/10  4/5
Creating equivalent fractions
using division.
1. Divide the numer. and
denom. by the same number.
Simplest Form
A fraction which can no longer
be simplified.
2/5, 3/4, 1/6, 2/3, 1/3
1/2, 1/9, 1/10, 3/5, 1/4
Convert Decimals to
Percents
.55 = 55% .7 = 70% 1.34 =
134%
Move the decimal point two places
to the RIGHT and then ADD the
percent sign.
Convert Percents to
Decimals
72% = .72 40% = .4 202%=2.02
Move the decimal point two places
to the LEFT and then DROP the
percent sign.
Adding Two Negative
Numbers
-4 + -5 = ?
1. Simply add the two
numbers together and
place the negative sign in
front.
-4 + -5 = -9
-12 + -6 = -18
-90 + -30 = -120
Order of Operations
This order must always be
followed when solving a problem.
1. Parentheses ( )
2. Exponents 4^3, 5^2, 9^4
3. Multiply and divide starting
from the left and moving right
4. Add and subtract starting
from left and moving right
Area
The space inside a polygon or how
much space a polygon takes up.
Area of rectangle or square= l * w
A. rect. or sq. = length times width
Perimeter
The distance around the outside of
a polygon.
Perimeter = sum of all the sides
Volume= l * w * h
Volume = length * width * height
Data Landmarks
Maximum-The greatest value
Minimum-The least value
Range-Max minus Min
Mode-The value that occurs
the most
Median-The middle value; Put the
numbers in numerical order and
then cross them out, start by going
least then greatest.
Mean-The average; Add up all the
values then divide by how many
were added up.
Surface Area
surface area-the sum of the
areas of the surfaces of a
polygon
surface area = add up the
areas of each side of a polygon
Volume Cont.
Volume for a cylinder
V = area of base * height (B * h)
Volume for rectangular
prism or cube
Area of triangle= ½ * b * h
Area of triangle = ½ * base * height
Coordinate grid
Volume
Very similar to Area, but for a
3-dimensional shape. Volume is
how much a 3-D shape can hold
inside of it.
Metric Units
Base Units-meter(m), liter (l),
gram (g)
milli- .001 of a m.; 1000mm=1 m.
centi- .01 of a m.; 100cm=1 m.
deci- .01 of a m. 10dm=1 m.
meter-base unit
kilo-1000 m. 1km = 1000m
Properties of circles
radius (r)-a line that goes from
the center of a circle to the edge
diameter (d)- a line that goes
from one edge of a circle to
another and passes through the
center; equal to 2 radii
Customary measurements
Length
12 inches (in.) = 1 foot (ft.)
3 ft. = 1 yard (yd.)
5280 ft. = 1 mile (mi.)
Weight
16 ounces (oz.) =1 pound (lbs.)
2000 lbs. = 1 ton
Capacity or Volume
8 fluid oz. = 1 cup (c.)
2 c. = 1 pint (pt.)
4 c. or 2 pt. = 1 quart (qt.)
4 qt. or 8 pt. or 16 c. = 1 gallon
Volume for a pyramid or cone
V = 1/3 * area of base * height
Area and Circumference
of Circles
 = about 3.14
Area =  * r^2
Circumference = 2 *  * r
Circumference-distance around a
circle; similar to perimeter
Ways to Express Numbers
625
Expanded Notation
600 + 20 + 5
Scientific Notation
6.25 x 10^2
Exponential Notation
5^4
Prime Factorization
5x5x5x5
Standard Notation
625
Greatest Common Factor (GCF)
1. List all the factors for both
numbers. Whichever one is the
greatest that they have in common
is the GCF.
15 - 1, 3, 5, 15
25 – 1, 5, 25
5 is the GCF for 15 and 25
Least Common Multiple (LCM)
1. List multiples until the two
numbers have one in common.
3- 3, 6, 9, 12, 15, 18, 21, 24
5-5, 10, 15, 20, 25
15 is the LCM for 3 and 5
Triangles
scalene-no sides are equal
isosceles-two or more sides
are equal
equilateral-all three sides
are equal
right-a triangle with a right
angle in it
Probability
Probability-the chances of an
event occurring
3-Dimensional Shapes
Cube
Cylinder
Rectangular Prism
Cone
1/8 chance of it landing on a “1”
3-Dimensional Shapes Cont.
Rectangular Pyramid Sphere
Triangular Pyramid Tri. Prism
¼ chance of it landing on an even #
3/8 chance of it landing on a “3,”
“4,” or “5.”
8/8 chance of it landing on a # “1-8”
0/8 chance of it landing on “9”
Polygons & Angle Measures
3 sides-triangle, sum of angles; 180
4 sides-quadrilateral, sum of angles;
360
5 sides-pentagon, sum of angles;
540
6 sides-hexagon, sum of angles; 720
7 sides-heptagon, sum of angles;
900
8 sides-octagon, sum of angles;
1080
Angles
Quadrilaterals
acute-measures between 0 and
90
parallelogram-two sets of parallel
sides.
right-measures exactly 90
rhombus-2 sets of parallel sides, all
side are equal length.
obtuse-measures between 90
and 180
straight-measures exactly 180
rectangle-2sets of parallel sides, all
angles are right angles.
square-2 sets of parallel sides, all
sides are equal length, all angles are
right.
trapezoid-1 set of parallel sides