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