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 Percents DiscountsA discount is an amount that is subtracted from the regular price of an item. discount = price discount rate total cost = price – discount TipsA tip is an amount added to a bill for service. tip = bill tip rate total cost = bill + tip Sales taxSales 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 Number 70% x $30.00 (.7) x 30

Pay 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 (.10) = 3.50 Discount = $3.05 Step 2: subtract discount from original price – 3.05 = 27.45

Pay More!

Elly is buying a dog bed for $ The sales tax rate is 7%. About how much will the total cost of the dog bed be? Step 1: Find 7% of (.07)=2.80 Step 2: Add to total bill to find the amount he paid! = $42.80

Pay More!

Joseph’s dinner bill from Longhorns is $ 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 (.15) = 2.68 Step 2: Add to total bill to find the amount he paid = $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 % = 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 % 3/10 2/5 3/25 99/ /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 %= =0.20

You try…Percent to Decimal 6) 12 % 7) 8 % 8) 75 % 9) 48 % 10) 120 %

Fractions to Percents CONVERSION 3

Setting it up Set up a ratio!!!

What percent is 5/40? 5 40 = P · P = 5 · P = = 12.5 %

Your turn… 11) 4/100 12) 2/5 13) 3/4 14) 2/3 15) 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 = = 3 10 = P P = P = 30 % = 43 %

Complete Table DecimalFractionPercent.01 4/23 78%

Unit #2 Scale Factor

Matching sides of two or more polygons are called corresponding sides Matching angles are called corresponding angles.

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 ___ ____ = Write a proportion using corresponding side lengths. The cross products are equal = 100 y The two triangles are similar. Find the missing length y

y is multiplied by ,200 = 100y 22, ______ 100y 100 ____ = Divide both sides by 100 to undo the multiplication. 222 mm = y

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 sideturns intoresulting side written as a ratio in this form:

Indirect Measurement Indirect Measurement uses similar figures and proportions to find height of objects you cannot measure directly

Word Problems 1. Underline the question 2. Set up your answer 3. 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 question Step 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.

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 question Step 2: Set up your answer: The Rocket is __________tall.

Step 3: Draw it out Step 4: Find the triangles

____ h 4 __ = = h = 3h ___ 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.

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.

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?

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 cm 5 cm 7cm 6 cm

Question #2 Determine if the ratios are proportional. Explain. 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 $ 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?

Question #7 If all angles are congruent, are these two shapes SIMILAR Yes! The cross products are equal! 54=54 OR 3/9 is equal to 6/18 Scale Factor = 2

Question #8

Answer

Question #9 Is this a proportion? 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 = 15/5 SF: 3

Use what you know about corresponding sides to find the scale factor.

Scale Factor 300 answer: 20/24 = 10/12 Reduce SF: 5/6

Is rectangle ABCD~EFGH?

Similar Figures 500 Answer: No 15/20 = 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 center of the figure out through identical places in the figure. Count the number of lines drawn. 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 turn is 180°. 1 2 __ ° 180° 360°

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 symmetry 360 ÷ 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 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 UnitAbbreviationBenchmark Inchin.Width of your thumb FootftDistance from your elbow to your wrist YardydWidth of a classroom door milemiTotal length of 18 football fields

What unit of measure would provide the best estimate? A doorway is about 7_____________high

Customary Units of Weight UnitAbbreviationBenchmark OunceozA slice of bread PoundlbA loaf of bread TonTA small car

What unit of measure would provide the best estimate? A bike could weigh 20 _____?

Customary Units of Capacity UnitAbbreviationBenchmark Fluid ouncefl ozA spoonful CupcA glass of juice PintptA small bottle of salad dressing QuartqtA small container of paint GallongalA large container of milk

What unit of measure would provide the best estimate? A large water cooler holds about 10 _____ of water.

Customary Conversion Factors 1 foot = 12 inches 1 yard = 3 feet 1 yard = 36 inches 1 mile = 5,280 feet 1 mile = 1,760 yards 1 pound (lb) = 16 ounces (oz) 1 Ton (T) = 2,000 pounds 1 gallon = 4 quarts 1 quart= 2 pints 1 pint = 2 cups 1 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 Same measurements in the denominator

How many feet are in 3 miles?

A book weighs 60 ounces. How many pounds is this?

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.

Length UnitAbbreviationRelation to a meterBenchmark Millimetermm.001 mThickness of a dime Centimetercm.01 mWidth of a fingernail Decimeterdm.1mWidth of a CD case Meterm1 mWidth of a single bed KilometerKm1,000 mDistance around a city block

Mass UnitAbbreviationRelation to a gram Benchmark Milligrammg.001 gVery small insect Gramg1 gLarge paper clip Kilogramkg1,000 gTextbook

Capacity UnitAbbreviationRelation to a liter Benchmark MillilitermL.001 LA drop of water LiterL1 LBlender 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 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 ², cm², etc.

#1 Find the area of the figure Write the formula. Substitute 15 for l. Substitute 9 for w. A = lw A = 15 9 A = 135 The area is about 135 in in. 9 in.

A parallelogram is a quadrilateral with opposite sides that are parallel.

Base Height

AREA OF A TRIANGLE b A = 1212 bh The area A of a triangle is half the product of its base b and its height h. h

Find the area of the triangle. A = 1212 bh Write the formula. A = 1212 (20 · 12) Substitute 20 for b and 12 for h. A = 120 The area is 120 ft 2. A = 1212 (240) Multiply.

Estimate the area of the circle. Use 3 to approximate pi. A ≈ A ≈ 1200 m m A = r 2 Write the formula for area. Replace  with 3 and r with 20. A ≈ Use the order of operations. Multiply.

Estimate the area of the circle. Use 3 to approximate pi. r = 28 ÷ 2 A ≈ m A = r 2 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 m 2 Multiply.

5 ft Question 1 Find the Area 17 ft Answer: 85 ft ²

r = 20 ÷ 2 A ≈ m A = r 2 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 m 2 Multiply. Question 2 Find the Area

Find the area of the triangle. A = 1212 bh Write the formula. A = 54 The area is 54 in 2. A = 1212 (108) Multiply. 24 ft 4 ft 1 2 A = 1212 (4 24) 1 2 Substitute 4 for b and 24 for h. 1 2 Question 3 Find 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

Base A side of a polygon; a face of a three dimensional figure by which the figure is measured or classified.

Prism A polyhedron that has two congruent, polygon shaped bases and other faces that are all rectangles.

Prism named after what kind of BASE it has

Pyramid A polyhedron with a polygon base and triangular sides that all meet at a common vertex.

Pyramid named after what kind of BASE it has

Cylinder A three dimensional figure with two parallel, congruent circular bases connected by a curved lateral surface.

Cone A three dimensional figure with one vertex and one circular base.

Cube A 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