“Rational Number Riddles”

Complete the Project worksheet “Rational Number Riddles.” Once you have completed #1 a-h, complete #2 and create your own riddles. Make sure you also come up

with the solutions.

C. 7/8 H. 73/200 A. 11/30 R. 5/12 C. 19/40 O. 17/25 A. 87/100 L. 7/8

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 6.4 “Similar and Congruent Figures”Section 6.4 “Similar and Congruent Figures”

Section 6.5 “Similarity and Measurement”Section 6.5 “Similarity and Measurement”

Section 6.6 “Scale Drawings”Section 6.6 “Scale Drawings”

Section 6.7 “Probability and Odds”Section 6.7 “Probability and Odds”

Section 6.8 “The Counting Principle”Section 6.8 “The Counting Principle”

Do Now

In your notebook, name several sports teams in which an athlete’s success is described in terms of his or her number of successes at some task.

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

Puzzler

A rope ladder is hanging over the side of a boat so that half of the ladder is under water. The tide is rising at a rate of 8 inches per hour. In how many hours will the entire ladder be under water? Explain.