Transcript 6.1 - Mathmatuch

“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
Probability”
Section 6.1 “Ratios and Rates”
Section 6.2 “Writing and Solving Proportions”
Section 6.3 “Solving Proportions Using Cross Products”
Section 6.4 “Similar and Congruent Figures”
Section 6.5 “Similarity and Measurement”
Section 6.6 “Scale Drawings”
Section 6.7 “Probability and Odds”
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.
Objective

SWBAT find ratios and unit rates
Section 6.1 “Ratios and Rates”
RATIOuses division to compare two
quantities of the SAME
MEASURE.
You can write ratios three different ways:
a to b
a:b
a
b
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…
VOLLEYBALL
A volleyball team plays 14 home matches and 10 away
matches.
a.
Find the ratio of home matches to away matches.
b.
Find the ratio of home matches to all matches.
SOLUTION
home matches
7
14
a.
= 10 = 5
away matches
b.
home matches
all matches
=
14
14
7
14 + 10 = 24 = 12
RATIOa comparison of two numbers by
division. The two numbers must have the
same unit of measure.
5 ft
Find the ratio of the
height to the width.
9 ft
Find the ratio of the
width to the height.
Are the ratios the same?
5
9
NO!!
9
5
Find the Ratio…
On a set of house plans, an architect wants to represent
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?
A comparison of two numbers by division.
The two numbers must have the same unit of measure
Length of segment
5 inches
Length of room
30 ft
(x 12 inches) =
5
1
360
72
Convert feet to inches.
12 inches in 1 foot.
The ratio is 1 to 72.
“Rates”
RATEa fraction in which the numerator and the
denominator have different units of
measure.
Examples of rates: speed & distance, wages
45miles
hour
5 meters
second
8 dollars
hour
UNIT RATEa rate with a denominator of
90miles
2 hours
÷2
=
÷2
=
1
45 miles
1 hour
UNIT RATE
Finding a Unit Rate
A car travels 110 miles in 2 hours. Find the unit rate.
110 miles
2 hours =
110 miles
2 hours
2
55 miles
2 = 1 hour
Finding a Unit Rate
Arnold and Jena went mountain biking on some trails
in their town. Based on the information below, which
one of them rode at a faster pace?
Arnold rode 23 miles in 4 hours.
Jena rode 16 miles in 3.5 hours.
Arnold
23 miles
4 hours =
23 miles
4 hours
4
5.75 miles
4 = 1 hour
Jena
16 miles
3.5 hours
16 miles ÷ 3.5
3.5 hours ÷ 3.5
4.6 miles
1 hour
Your basic monthly charge for cell phone service is $30, which
includes 300 free minutes. You pay a fee for each extra minute you use.
One month you paid $3.75 for 15 extra minutes. Find your total bill if you
use 22 extra minutes.
STEP 1 Calculate the unit rate.
3.75
15
0.25
=
1
= $.25 per minute
STEP 2
Write a verbal model and then an expression. Let m be the number of
extra minutes.
30
+
0.25
m
STEP 3
Evaluate the expression when m = 22.
30 + 0.25(22) = 35.5
Total Bill: $35.50
“Rate or Ratio?”
8 people
11 people
140 gallons
5 min utes
16apples
3apples
80beats
1 min ute
10miles
2hours
Rate
85 ft
13inches
Ratio
Writing Equivalent Rates
5 m ? m

1 sec 1 h
If you are walking 5
meters in 1 second, how
many meters will you
walk in a hour?
There are 60 seconds in
a minute and 60 minutes
in a hour, so multiply 5
meters by 3600.
5 m 18,000 m

1 sec
1h
3 lb ? oz

$1
$1
If you can buy 3 pounds
for a $1, how many
ounces can you buy for a
$1?
There are 16 ounces in a
pound, so multiply 3
pounds by 16.
3 lb 48 oz

$1
$1
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.