Download - Qtr. 3 Interim Review
UNIT #1 PERCENTS, DECIMALS
AND FRACTIONS
Qtr. 3 Interim Review
Using Percents in the Real World
Percentages are commonly used in everyday life. When you pay for something, whether it is a product or a service, percents are almost always involved. Most often percents are used to calculate discounts, tips, and sales tax.
Common Uses of PercentsDiscounts A discount is an amount that is
subtracted from the regular price of an item. discount = price • discount rate total cost = price – discount
Tips A tip is an amount added to a bill for service. tip = bill • tip rate total cost = bill + tip
Sales tax Sales tax is an amount added to the price of an item.
sales tax = price • sales tax rate total cost = price + sales tax
Basic Skill
Percent x Number70% x $30.00
(.7) x 30
DiscountsPay Less!
American Eagle is having a 10% off sale. If Chandler wants to buy a sweater whose regular
price is $30.50, about how much will she pay for the sweater after the discount?
Step 1: Find 10% of 30.50
30.50(.10) = 3.50Discount = $3.05
Step 2: subtract discount from original price.
30.50 – 3.05 = 27.45
Sales Tax
Pay More!
Elly is buying a dog bed for $40.00. The sales tax rate is 7%.
About how much will the total cost of the dog bed be?
Step 1: Find 7% of 40.00
40(.07)=2.80
Step 2: Add to total bill to find the amount he paid!
40 + 2.80 = $42.80
TipsPay
More!
Joseph’s dinner bill from Longhorns is $17.85. He wants to leave a tip that is 15% of the bill. About how much should his tip be? How much will he
have to pay total?Step 1: Find 15% of 17.85
17.85(.15) = 2.68
Step 2: Add to total bill to find the amount he paid
2.68 + 17.85 = $20.83
Problem #1
About how much do you save if a book whose regular price is $25.00 and is on sale for 10%
off?
Problem #2
Julie gets a 15% discount on all of the items in the clothing store where she works. If she buys a shirt that regularly costs $44.99, how much
money will she save with her employee discount?
Problem #3
A bead store has a sign that reads “20% off the regular price.” If Janice wants to buy beads that regularly cost $6.00,how much will she pay for
them after the store’s discount?
Problem #4
At Paint City, a gallon of paint with a regular price of $17.99 is now 15% off. At Giant Hardware, the same paint usually costs $21.99, but is now 20% off. Which store is offering the better deal?
What is a percent?A percent is a ratio…how many
times out of a hundered
45 %
= 45100
45 percent means 45 out of
100 possible times!
Percents to Fractions
CONVERSION 1
Percentages can be written as a fraction
by simply placing them over 100!
Write these percents as fractions. Be sure to simplify
1)30 %2)40 %3)12 %4)99 %5)101 %
3/102/53/2599/1001 1/100
Dude…That was
easy
Percents to Decimals
CONVERSION 2
Steps
Since I can put all percents over a hundred then all I need to do is write the equivalent decimal.
Move your decimal place over to the LEFT twice!
20 % = 20100
= 0.20
You try…Percent to Decimal
6)12 %7)8 %8)75 %9)48 %10)120 %
0.120.080.750.481.20
Fractions to Percents
CONVERSION 3
Setting it up
Set up a ratio!!!
100xFraction
What percent is 5/40?
540
= P100
40 · P = 5 · 10040P = 50050040
= 12.5 %
100xFraction
Your turn…
11)4/10012)2/513)3/414)2/315)2 1/2
4 %40 %75 %66.6 %250 %
Decimals to Fractions
CONVERSION 4
Steps
Whatever place value the fraction ends in is your DENOMINATOR
Make sure to simplify! From here you can go easily into
PERCENTS!!!!
Why is that?
0.43 = 10043
0.3 = 310 = P
100
10P = 30030010
P = 30 %
= 43 %
Complete Table Decimal Fraction Percent
.014/23
78%
Unit #2 Scale Factor
Matching sides of two or more polygons are called corresponding sidesMatching angles are called corresponding angles.
Similar FiguresTwo figures are similar if• the measures of the corresponding angles are equal• the ratios of the lengths of the corresponding sides are proportional
Similar figures have the same shape but not necessarily the same size.
Finding missing angles
Hint: Remember angles are the same in corresponding angles!
What is angle D? <D
Finding Missing lengths
111 y
___ 100 200
____ = Write a proportion using corresponding side lengths.
The cross products are equal.200 • 111 = 100 • y
The two triangles are similar. Find the missing length y
y is multiplied by 100.22,200 = 100y
22,200 100
______ 100y 100
____ = Divide both sides by 100 to undo the multiplication.
222 mm = y
ScaleFactor
The Recipe
Scale Factor a rate of change for corresponding sides one side will be given, and it will change into its
corresponding side given side turns into resulting side
written as a ratio in this form:
𝑟𝑒𝑠𝑢𝑙𝑡𝑖𝑛𝑔𝑠𝑖𝑑𝑒𝑔𝑖𝑣𝑒𝑛𝑠𝑖𝑑𝑒
Indirect Measurement
Indirect Measurement uses similar figures and proportions to find height of objects you cannot
measure directly
Word Problems 1. Underline the question2. Set up your answer3. Draw it out 4. Find the similar shapes in your
drawing (triangles) 5. Use similar figures and proportions
to solve your problem!!!!
A tree casts a shadow that is 7 ft. lawn. Ken, who is 6 ft tall, is standing next to the tree.
Kens has a 2-foot long shadow. How tall is the tree?
Step 1: underline the questionStep 2: Set up your answer: The tree is __________tall.
Step 3: Draw it out
Step 4: Find the triangles
2 7
__ 6 h
__ =
h • 2 = 6 • 7 2h = 42 2h 2
___ 42 2
___ =
h = 21
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
The tree is 21 feet tall.
Step 5: Proportions
Example #2
ROCKETS
A rocket casts a shadow that is 91.5 feet long. A 4-foot
model rocket casts a shadow that is 3 feet long. How tall is
the rocket?
Step 1: underline the questionStep 2: Set up your answer: The Rocket is __________tall.
Step 3: Draw it out Step 4: Find the triangles
91.5 3
____ h 4
__ =
4 • 91.5 = h • 3 366 = 3h
366 3
___ 3h 3
___ =
122 = h
Write a proportion using corresponding sides.
The cross products are equal.
h is multiplied by 3.Divide both sides by 3 to undo multiplication.
The rocket is 122 feet tall.
Step 5: Proportio
ns
The map shown is a scale drawing. A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object. In other words, measurements on a scale drawing are in proportion to the measurements of the real object.
SCALE
Is it set up right?Why or why not?
1. The scale on the map is 3 cm: 10 m. On the map the distance between two cities is 40 cm. What is the actual distance?
2. The scale on the map is 10 in: 50. On the map the distance between two schools is 30 in. What is the actual distance?
3 1040 x
10 3050 x
NO
Yes
The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual
distance? 20 in. x mi
_____ 4 in. 1 mi
____ =
1 • 20 = 4 • x 20 = 4x 20 4
___ 4x 4
___ = 5 = x
Write a proportion using the scale. Let x be the actual number of miles between the two towns.The cross products are equal.
x is multiplied by 4.
Divide both sides by 4 to undo multiplication.
5 miles
Question #1 Find side GF
10 cm5 cm
7cm
6 cm
Answer: 12 cm
Question #2 Determine if the ratios are proportional. Explain.
92 23121 34
No, cross proportions don’t equal (2783 doesn’t equal 3128)
Question #3
You want to leave your server a 20% tip. The total bill
comes to $54.50. How much should you leave for a tip?
$10.90
Question #4 A scale on a map reads 5 in: 50 miles. If two lakes
are 11 inches apart on the map, what is the actual
distance?
110 Miles
Question #5
How do you know if two figures are
SIMILAR?Angles are the EXACT SAME. Side lengths have to
be proportionally similar
Question #6 On a sunny afternoon, a
goalpost casts a 70 ft shadow. A 6 ft football player next to the goal post has a shadow 20 ft long. How tall is the
goalpost?
21 ft
Question #7 If all angles are congruent, are
these two shapes SIMILAR
39
6
18Yes!
The cross products are equal! 54=54
OR 3/9 is equal to 6/18Scale Factor = 2
Question #8
< A ___________
EF ___________
BA __________
<F ___________
Answer
< A __<D_________
EF ____BC_______
BA ____ED______
<F ____<C_______
Question #9
Is this a proportion?
2520
108
Yes!
The cross products are equal! 200=200
Question #10
The following rectangles are similar. What is the length of
side RS?
Question #11 A postcard is 6 inches wide and 14 inches long. When the postcard is
enlarged, it is 10 inches wide.
What is the length of the enlarged postcard?
Figure A is the original. Find the
scale factor.
Scale Factor 200 answer:
9/3 = 15/5SF: 3
Use what you know about corresponding sides to find the scale
factor.
Scale Factor 300 answer:
20/24 = 10/12ReduceSF: 5/6
Is rectangle ABCD~EFGH?
A B
CDE
F G
H
1520
25
30
Similar Figures 500Answer:
No15/20 = 25/30
¾ will not equal 5/6
Unit #3
ROTATIONAL SYMMETRY
Review
• A figure has rotational symmetry if, when it is rotated (turned) less than 360° around a central point, it coincides with itself (Looks exactly the same)
• The central point is called the center of rotation.
• A figure that coincides with itself after a rotation of 180° has rotational symmetry
Tell how many times each figure will show rotational symmetry within one full rotation.
Draw lines from the centerof the figure out throughidentical places in the figure.
Count the number of linesdrawn.
The figure will show rotational symmetry 4 times within a 360° rotation.
Degree of Rotation
The smallest number of degrees that a figure can be turned and still look identical to itself.
Trace the following figure. Rotate the figure and determine the degree of rotation (what degree does it start looking identical to the original?)
A rotation is the movement of a figure around a point. A point of rotation can be on or outside a
figure.
The location and position of a figure can change with a rotation.
A full turn is a 360° rotation. So a turn
is 90°, and a turnis 180°.
12__
14__
90°
180°
360°
Clockwise CounterClockwise
Finding the Degree of Rotation
Can be found by:
360° ÷ # of lines of symmetry
How many lines of symmetry does a the figure below
have?What’s the degree of rotation?
Symmetry 200
Answer: 5 lines of symmetry360 ÷ 5 =
72
Question
Draw a 180° counterclockwise rotation
Answer
Draw a 180° counterclockwise rotation
Question
Draw a 90° counterclockwise rotation
Answer
Unit #4 Measurement
The customary system is the measurement system used in the
United States. It includes units of measurement for
length, weight, and capacity.
WHAT IS IT?
What is a benchmark?
If you do not have an instrument, such as a ruler, scale, or measuring cup, you can estimate the length, weight, and capacity
of an object by using a benchmark. It helps you visualize actual
measurements!
Customary Units of Length
Unit Abbreviation Benchmark
Inch in. Width of your thumb
Foot ft Distance from your elbow to your wrist
Yard yd Width of a classroom door
mile mi Total length of 18 football fields
Lengths
What unit of measure would provide the best estimate?A doorway is about 7_____________high
Feet
Customary Units of WeightUnit Abbreviation Benchmark
Ounce oz A slice of breadPound lb A loaf of bread
Ton T A small car
Weight
What unit of measure would provide the best estimate?
A bike could weigh 20 _____?
lb.
CapacityCustomary Units of Capacity
Unit Abbreviation BenchmarkFluid ounce fl oz A spoonful
Cup c A glass of juicePint pt A small bottle of salad dressing
Quart qt A small container of paintGallon gal A large container of milk
What unit of measure would provide the best estimate?
A large water cooler holds about 10 _____ of water.
Gallons
Customary Conversion Factors1 foot = 12 inches1 yard = 3 feet1 yard = 36 inches1 mile = 5,280 feet1 mile = 1,760 yards1 pound (lb) = 16 ounces (oz)1 Ton (T) = 2,000 pounds1 gallon = 4 quarts 1 quart= 2 pints1 pint = 2 cups1 cup = 8 fluid ounces (fl oz)
To convert from one unit of
measurement to another unit of measurement,
use a proportion
Cool, we’ve been using this since November!
Important!
Same measurements in the numerator
And Same measurements in the denominator
inches inchesfeet feet
not feet inchesinches feet
How many feet are in 3 miles?
1 35,280 ?mile miles
ft
5,280 3 15,840 115,840 feet
A book weighs 60 ounces. How many pounds is this?
1 ?16 60poundounces ounces
1 60 60 163.75pound
Metric System:
King Henry Doesn’t Usually Drink Chocolate Milk
Memorize this!
Naming the Metric Units
Meter units measure Length
Gram units measure mass or weight
Liter units measure volume or capacity.
LengthUnit Abbreviation Relation to a
meterBenchmark
Millimeter
mm .001 m Thickness of a dime
Centimeter
cm .01 m Width of a fingernail
Decimeter
dm .1m Width of a CD case
Meter m 1 m Width of a single bed
Kilometer Km 1,000 m Distance around a city block
Mass
Unit Abbreviation
Relation to a gram
Benchmark
Milligram mg .001 g Very small insect
Gram g 1 g Large paper clip
Kilogram kg 1,000 g Textbook
Capacity
Unit Abbreviation
Relation to a liter
Benchmark
Milliliter
mL .001 L A drop of water
Liter L 1 L Blender Container
Example #1:
(1) Look at the problem. 56 cm = _____ mm
Look at the unit that has a number. 56 cm
On the device put your pencil on that unit. k h d U d c m
km hm dam m dm cm mm
Example #1:
k h d U d c m
km hm dam m dm cm mm
2. Move to new unit, counting jumps and noticing the direction of the jump!
One jump to the right!
Example #1:
3. Move decimal in original number the same # of spaces and in the same direction.
56 cm = _____ mm
56.0.
Move decimal one jump to the right. Add a zero as a placeholder.
One jump to the right!
Example #1:
56 cm = _____ mm
56cm = 560 mm
Question
¼ lb=________________oz
4
Question
8 cups =________________fl oz
16
Question
346 yards=________________inches
12,456 inches
Question
10 quarts =________________gal
2.5
Question
An average cat weighs
15__________(ounces, pounds, tons)
Pounds
Question
130 g = ________kg
.13 kg
Question
What would be a reasonable measurement for the distance from NGMS to NGHS
Customary
Mile
Question
How many pints are in a gallon?
8
Question
How long is the line?
3.5 inches
Unit #5 2-D & 3-D Figures
• The area of a figure is the amount of surface
it covers. • We measure area in
square units.• Example: in , cm , etc.² ²
6 cm
4 cm
A lw 224 6 4cm
Rectangles
#1 Find the area of the figure
Write the formula.
Substitute 15 for l.
Substitute 9 for w.
A = lw
A = 15 • 9A = 135
The area is about 135 in2.
15 in.
9 in.
A parallelogram is a quadrilateral with opposite sides that are parallel.
Base
Height
A=Bh
Why does this work?
9 cm
8 cm
4 cm
A bh 232 8 4cm
#1
AREA OF A TRIANGLE
b
A = 12bh
The area A of a triangleis half the product of itsbase b and its height h.
h
Or A=bh÷2
Find the area of the triangle.A = 12 bh Write the formula.
A = 12 (20 · 12) Substitute 20 for b and 12 for h.
A = 120The area is 120 ft2.
A = 12 (240) Multiply.
AreaOf
Circles
Estimate the area of the circle. Use 3 to approximate pi.
A ≈ 3 • 202
A ≈ 1200 m2
19.7 m
A = r2 Write the formula for area.Replace with 3 and r with 20.
A ≈ 3 • 400 Use the order of operations.
Multiply.
Estimate the area of the circle. Use 3 to approximate pi.
r = 28 ÷ 2
A ≈ 3 • 142
28 m
A = r2 Write the formula for area.
Replace with 3 and r with 14.
r = 14
Use the order of operations.
Divide.
r = d ÷ 2 The length of the radius is half the length of the diameter.
A ≈ 3 • 196A ≈ 588 m2 Multiply.
5 ft
Question 1
Find the Area
17 ftAnswer:
85 ft²
r = 20 ÷ 2
A ≈ 3 • 102
20 m
A = r2 Write the formula for area.
Replace with 3 and r with 10.
r = 10
Use the order of operations.
Divide.
r = d ÷ 2 The length of the radius is half the length of the diameter.
A ≈ 3 • 100A ≈ 300 m2 Multiply.
Question 2Find the Area
Find the area of the triangle.A = 12 bh Write the formula.
A = 54The area is 54 in2.
A = 12 (108) Multiply.
24 ft
4 ft12
A = 12 (4 • 24)12
Substitute 4 for b and 24 for h.
12
Question 3Find the Area
Unit #4 3-D Figures
-A closed plane figure formed by three or more line segments that intersect only at their endpoints
-A three dimensional figure in which all the surfaces are polygons
-A flat surface (polygon) on a solid figure
-The segment where two faces meet
-The point where three or more edges meet
BaseA side of a polygon; a face of a
three dimensional figure by which the figure is measured
or classified.
PrismA polyhedron that has two congruent, polygon shaped bases and other faces that are all rectangles.
Prism named after what kind of BASE it has
PyramidA polyhedron with a polygon base and
triangular sides that all meet at a common vertex.
Pyramid named after what kind of BASE it has
CylinderA three dimensional figure with two parallel, congruent circular bases connected by a curved
lateral surface.
ConeA three dimensional figure with one vertex and one circular base.
CubeA rectangular prism with six congruent square
faces.
Question
What is a 3-D shape that has 5
FACES
Pyramid
Which of the nets below could be used to form a pyramid like the one below?
Question