do now: 1) given triangle uaf with coordinates
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EQ: How do I use ratios to compare numbers. Do Now: 1) Given triangle UAF with coordinates U(O, 4), A(8, -9), and F(-IO, -12), find the image of point A after a reflection in the y-axis. - PowerPoint PPT PresentationTRANSCRIPT
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Do Now:1) Given triangle UAF with coordinatesU(O, 4), A(8, -9), and F(-IO, -12), find the image of point A after a reflection in the y-axis.
2) After a reflection in the y-axis, (-1,-1) is the image of point B. What is the original location of point B?
EQ: How do I use ratios to compare numbers
HWK: WB p 42, even, p43, odd:
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Learn to identify, write, and compare ratios and find units and compare unit rates, such as average speed and unit price. .
Course 2
5-1 Ratios, Rates and Unit Rates
M7P1.b Solve problems that arise in mathematics and in other contexts; M7P1.d Monitor and reflect on the processof mathematical problem solving
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Vocabulary
A ratio is a comparison of two quantities by division.
Insert Lesson Title Here
Course 2
5-1 Ratios
A rate is a ratio that compares two quantities measured in different units.
A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator.
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Course 2
5-1 Ratios
Sometimes a ratio can be simplified. To simplify a ratio, first write it in fraction form and then simplify the fraction.
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Course 2
5-1 Ratios
To compare ratios, write them as fractions with common denominators. Then compare the numerators.
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Course 2
5-2 Rates
An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different.
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In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the
ratio . A ratio is a comparison of two
quantities by division.
1725
Kathlene can write her ratio of baskets madeto attempts in three different ways.
1725
17 to 25 17:25
Course 2
5-1 Ratios
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Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.
Course 2
5-1 Ratios
A. rock to hip hop
57
, 5 to 7, 5:7
The ratio of rock to hip hop is 5 to 7, which can be written as follows:
B. hip hop to popThe ratio of hip hop to pop is 7 to 8, which can be written as follows:78
, 7 to 8, 7:8
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Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.
Course 2
5-1 Ratios
C. rock to pop and hip hop
The ratio of rock to pop is 5 to 8 and rock to hip hop is 5 to 7, which can be written as follows:
515
, 5 to 15, 5:15
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Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.
Course 2
5-1 Ratios
A. snow boarding to rock climbing
69
, 6 to 9, 6:9
The ratio of snow boarding to rock climbing is 6 to 9, which can be written as follows:
B. kite surfing to snow boardingThe ratio of kite surfing to snow boarding is 4 to 6, which can be written as follows:46
, 4 to 6, 4:6
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Course 2
5-1 Ratios
C. rock climbing to kite surfing and snowboarding
The ratio of rock climbing to kite surfing is 9 to 4 and rock climbing to snow boarding is 9 to 6, which can be written as follows:
910
, 9 to 10, 9:10
Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.
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On average, most people can read about 600 words in 3 minutes. Write the ratio of words to minutes in all three forms. Write your answer in simplest form.
Course 2
5-1 Ratios
wordsminute
Write the ratio as a fraction.
600 ÷ 33 ÷ 3
= 6003
Simplify.
For every minute, there are 200 words read.
wordsminute
=
wordsminute
= 2001
The ratio of words to minutes is 200 to 1.
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At Casitas Middle School there are 456 microscopes for 152 students. Write the ratio of microscopes to students in all three forms. Write your answer in simplest form.
Course 2
5-1 Ratios
microscopesstudents
Write the ratio as a fraction.
456 ÷ 152152 ÷ 152
= 456152
Simplify.
For every microscope, there are 3 children.
microscopestudents
=
microscopestudents
= 31
The ratio of microscopes to students is 3 to 1.
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Honey-lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Compare the ratio of drops per ounces for each bag of cough drops.
Course 2
5-1 Ratios
Honey-lemon Cherry
Drops 30 24
Ounces 10 6
Honey-lemon: dropsounces
= 3010
= 31
Cherry: dropsounces
= 246
= 41
Because 4 > 3 and the denominators are the same, the drops to ounces is greater in the bag of cherry cough drops.
Write the ratios as fractions with common denominators.
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Jelly beans come in small packages of 25 per 5 ounce package and large packages of 56 per 8 ounce package. Compare the ratio of jelly beans per ounce for each of the packages.
Course 2
5-1 Ratios
Large Small
Jelly beans 56 25
Ounces 8 5
Large:jelly beans ounces
= 568
= 71
Small: jelly beans ounces
= 255
= 51
Because 7 > 5 and the denominators are the same, jelly beans to ounces is greater in the small package.
Write the ratios as fractions with common denominators.
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Find the rate.
A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?
105 minutes35 revolutions
Write a rate that compares minutes and revolutions.
Simplify.
Divide the numerator and denominator by 35.
Course 2
5-2 Rates
105 minutes ÷ 35 35 revolutions ÷ 35
3 minutes1 revolution
The Ferris wheel revolves 1 time in 3 minutes.
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Find the rate.
Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?
24 lights6 yards
Write a rate that compares security lights and yards.
Simplify.
Divide the numerator and denominator by 6.
Course 2
5-2 Rates
24 lights ÷ 6 6 yards ÷ 6
4 lights1 yard
Sue passes 4 security lights in 1 yard.
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Find the rate.
A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute?
696 steps12 minutes
Write a rate that compares steps and minutes.
Simplify.
Divide the numerator and denominator by 12.
Course 2
5-2 Rates
696 steps ÷ 12 12 minutes ÷ 12
58 steps1 minute
The dog walks 58 steps per minute.
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Find the rate.
To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?
30 cups of ice12 smoothies
Write a rate that compares cups of ice and smoothies.
Simplify.
Divide the numerator and denominator by 12.
Course 2
5-2 Rates
30 cups of ice ÷ 12 12 smoothies ÷ 12
2.5 cups of ice1 smoothie
Henry needs 2.5 cups of ice per smoothie.
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Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour?
68 miles4 hours
Write the rate as a fraction.
68 miles ÷ 4 4 hours ÷ 4
= 17 miles1 hour
Divide the numerator and denominator by the denominator
Danielle’s average speed should be 17 miles per hour.
Course 2
5-2 Rates
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Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour?
1191 miles3 hours
Write the rate as a fraction.
1191 miles ÷ 3 3 hours ÷ 3
= 397 miles1 hour
Divide the numerator and denominator by the denominator
Rhett’s average speed should be 397 miles per hour.
Course 2
5-2 Rates
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A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples.
Course 2
5-2 Rates
Type of Item Example of Units
Liquid Ounces, quarts, gallons, liters
Solid Ounces, pounds, grams, kilograms
Any item Bottle, container, carton
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A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?
Consumer Math Application
Size Price
12 ounces $0.99
16 ounces $1.19
Divide the price by the number of ounces (oz) to find the unit price of each size.
$0.9912 oz
≈ $0.08oz
Since $0.07 < $0.08, the 16 oz sports drink is the best buy.
Course 2
5-2 Rates
$1.1916 oz
≈ $0.07oz
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A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy?
Size Price
1.5 gal $4.02
3.5 gal $8.75
Divide the price by the number of gallons (g) to find the unit price of each size.
$4.021.5 gal
= $2.68gal
Since $2.50 < $2.68, the 3.5 gallon container is the best buy.
Course 2
5-2 Rates
$8.753.5 gal
= $2.50gal
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TOTD
A coin bank contains 16 quarters, 12 dimes, and 8 nickels.
Insert Lesson Title Here
Course 2
5-1&2 Ratios and Rates
1. nickels to quarters
2. On a school trip, Bus 1 has 3 teachers and 14 students. Bus 2 has 4 teachers and 28 students. Which bus has the greater ratio of teachers to students?
3. There are 220 calories in 5 crackers. Write the ratio of calories to crackers in all three forms. Write your answers in simplest form.