do now 3/28/11 copy hw in your planner. copy hw in your planner. text p. text p. 272, #10-36 evens...
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Do Now 3/28/11Do Now 3/28/11
Copy HW in your planner.Copy HW in your planner.Text p. Text p. 272, #10-36 evens
Be ready to copy POTW #1 for the 4th marking period.
Chapter 6 “Ratio, Proportion, and Chapter 6 “Ratio, Proportion, and Probability”Probability”
Section 6.1 “Ratios and Rates”Section 6.1 “Ratios and Rates”
Section 6.2 “Writing and Solving Proportions”Section 6.2 “Writing and Solving Proportions”
Section 6.3 “Solving Proportions Using Cross Products”Section 6.3 “Solving Proportions Using Cross Products”
Section 6.7 “Probability and Odds”Section 6.7 “Probability and Odds”
Section 6.8 “The Counting Principle”Section 6.8 “The Counting Principle”
ObjectiveObjective
SWBAT find ratios and unit ratesSWBAT find ratios and unit rates
RATIO-RATIO- uses division to compare two
quantities of the SAME MEASURE.
a to ba to b a:ba:b aabb
You can write ratios three different ways:You can write ratios three different ways:
Section 6.1 “Ratios and Rates”
Ratios
What is the ratio of: Blue to total Yellow to green green to red Red to blue
1/17 6/7 7/3 3/1
Try It Out…Try It Out…
SOLUTIONSOLUTION
VOLLEYBALLVOLLEYBALL
A volleyball team plays A volleyball team plays 1414 home matches and home matches and 1010 away away matchesmatches..
a.a. Find the ratio of home matches to away matches.Find the ratio of home matches to away matches.
== 7755a.a.
home matcheshome matches
away matchesaway matches
1414 1010 ==
b.b. Find the ratio of home matches to all matches.Find the ratio of home matches to all matches.
b.b.home matcheshome matches
all matchesall matches
1414 14 + 1014 + 10
== == 14142424 ==
771212
RATIO-RATIO-a comparison of two numbers by a comparison of two numbers by
division. The two numbers must have the division. The two numbers must have the same unit of measure. same unit of measure.
5 ft
9 ft
Find the ratio of the height to the width.
Find the ratio of the width to the height.
Are the ratios the same?
9
55
9
NO!!
Find the Ratio…On a set of house plans, an architect wants to representOn a set of house plans, an architect wants to representa 30ft length of a room by a 5 inch segment. What is the a 30ft length of a room by a 5 inch segment. What is the ratio of the length of the segment to the length of the room?ratio of the length of the segment to the length of the room?
Length of segmentLength of segment 5 inches5 inches 55
Length of roomLength of room 30 ft30 ft
11
7272(x 12 inches) = 360(x 12 inches) = 360
The ratio is 1 to 72.The ratio is 1 to 72.
A comparison of two numbers by division. A comparison of two numbers by division. The two numbers must have the The two numbers must have the same unit of measuresame unit of measure
Convert feet to inches.Convert feet to inches.12 inches in 1 foot.12 inches in 1 foot.
a fraction in which the numerator and the a fraction in which the numerator and the denominator have different units of denominator have different units of measure. measure.
Examples of rates: speed & distance, wagesExamples of rates: speed & distance, wages
45miles45miles hourhour
5 meters5 meters secondsecond
8 dollars8 dollars hourhour
““Rates” Rates”
RATE-RATE-
a rate with a denominator of
90miles90miles 2 hours2 hours
45 miles45 miles 1 hour1 hour
UNIT RATE-UNIT RATE-11
==UNIT RATEUNIT RATE
÷ 2÷ 2÷ 2 ÷ 2 ==
Finding a Unit RateFinding a Unit Rate
A car travels A car travels 110110 miles in miles in 22 hours. Find the unit rate. hours. Find the unit rate.
110110 milesmiles 22 hourshours == 11 hourhour
5555 milesmiles22 hourshours 22
110110 milesmiles 22 ==
Finding a Unit RateFinding a Unit Rate Arnold and Jena went mountain biking on some trails Arnold and Jena went mountain biking on some trails in their town. Based on the information below, whichin their town. Based on the information below, whichone of them rode at a faster pace?one of them rode at a faster pace?
2323 milesmiles 44 hourshours == 11 hourhour
5.75 5.75 milesmiles44 hourshours 4 4
2323 milesmiles 44 ==
Arnold rode 23 miles in 4 hours.Arnold rode 23 miles in 4 hours.Jena rode 16 miles in 3.5 hours.Jena rode 16 miles in 3.5 hours.
16 miles 16 miles 16 miles 16 miles ÷ 3.5 4.6 miles÷ 3.5 4.6 miles
3.5 hours 3.5 hours 3.5 hours 3.5 hours ÷ 3.5 1 hour÷ 3.5 1 hour
ArnoldArnold
JenaJena
STEPSTEP 11 Calculate the unit rateCalculate the unit rate..
1515
3.753.75==
0.250.25
11 == $.25 $.25 per minuteper minute
Write a verbal model and then an expression. Let Write a verbal model and then an expression. Let mm be the number of be the number of extra minutesextra minutes..
STEPSTEP 22
30 + 0.25 30 + 0.25 mm
Evaluate the expression when Evaluate the expression when mm == 22.22.
30 + 0.25(22) = 35.530 + 0.25(22) = 35.5
STEPSTEP 33
Total Bill: $35.50Total Bill: $35.50
Your basic monthly charge for cell phone service is Your basic monthly charge for cell phone service is $30$30, which , which includes includes 300300 free minutes. You pay a fee for each extra minute you use. free minutes. You pay a fee for each extra minute you use. One month you paid One month you paid $3.75$3.75 for for 1515 extra minutes. Find your total bill if you extra minutes. Find your total bill if you use use 2222 extra minutes. extra minutes.
““Rate Rate or or Ratio?”Ratio?”
RateRate RatioRatio
people
people
11
8
inches
ft
13
85hours
miles
2
10
utes
gallons
min5
140
ute
beats
min1
80apples
apples
3
16
Writing Equivalent RatesWriting Equivalent Rates
If you are walking 5 If you are walking 5 meters in 1 second, how meters in 1 second, how many meters will you many meters will you walk in a hour?walk in a hour?
h
mm
1
?
sec1
5
There are 60 seconds in There are 60 seconds in a minute and 60 minutes a minute and 60 minutes in a hour, so multiply 5 in a hour, so multiply 5 meters by 3600. meters by 3600.
If you can buy 3 pounds If you can buy 3 pounds for a $1, how many for a $1, how many ounces can you buy for a ounces can you buy for a $1?$1?
1$
?
1$
3 ozlb
There are 16 ounces in a There are 16 ounces in a pound, so multiply 3 pound, so multiply 3 pounds by 16.pounds by 16.
h
mm
1
000,18
sec1
5
1$
48
1$
3 ozlb
Homework
Text p. 272, #10-36 evens, #44, & #47