Chapter 8x

Report
8-1: Ratios and
Equivalent Ratios
{
IWBAT read and write ratios and equivalent ratios
Ratio – A comparison of two quantities
9 girls and 7 boys
Three ways to write ratios:
1. 9:7
2. 9 to 7
3.
Ratio
9
7
Two ratios that are equal to each other
9 9 ∙ 5 45
=
=
7 7 ∙ 5 35
9 45
=
7 35
Equivalent Ratios
5:8 _____ 15:24
1) Rewrite as in fraction form and make
equal to each other
5 15
=
8 24
2) Cross-multiply (multiply diagonally)
120 = 120
3) If cross-products are equal, the ratios
are equivalent (=). If cross-products are
not equal (≠)
Are the ratios equivalent?
1)
3
12
9
____ 36
2)
108 = 108
4
6
16
______ 20
80≠96
3) 9 to 8 ____ 45 to 40
9
45
_____
8
40
360 = 360
Examples
8-2 and 8-3:
Proportions
{
IWBAT solve proportions using equivalent ratios
using Cross-Products (Cross-Multiplication)
4 12
,
5 15
Use the cross-multi plying method
4 12
,
5 15
60 = 60
Yes
Do these ratios make a proportion?
1)
3 9
,
8 21
63 ≠ 72
No
2)
2 18
,
3 27
3)
5 40
,
8 64
54 = 54
320 = 320
Yes
Yes
Examples
2

=
3 21
1) Simplify vertically and/or
horizontally, if possible
2 
=
1 7
2) Cross-multiply
 = 14
3) Solve for , if needed
Find the missing number
1)
6
9
8
=
2)
9
15

= 10
3)
8.5
3.2
=

8
5) Three boxes of cereal cost $10.50. What does one box cost?
Examples
4)
2.6

4
= 4.8
8-4: Too Much or Too
Little Information
{
IWBAT determine which information is missing
and identify extraneous information in problems.
8-5: Rates
{
IWBAT use rates to solve problems.


Rate – A ratio that compares two quantities that
have different units of measure
Unit Rate – A rate where the second quantity is
a unit of one (denominator)
Vocabulary
You travel 99 miles in 90 minutes. What is your average rate of speed in miles
per hour?
99 
90 
1) Write as a rate in fraction form
2) Divide
3) Rewrite as a phrase or as a fraction
with labels
9.5
9.5 miles per minute
9.5 

Find the Unit Rate
1) 90 miles in 75 minutes
2) 252 miles every 9 gallons
3) 48 chairs for 6 tables
4) 96 students in 3 classrooms
5) Respiration rate is the number of breaths you take per minute. You count
48 breaths in 3 minutes and your friend counted 34 breaths in 2 minutes. Who
had the higher respiration rate?
Examples
8-6: Unit Price
{
IWBAT find unit prices to determine the better
buy.

Unit Price – The cost per item


Similar to unit rate but money amount always is
the numerator
Round to the nearest cent (hundredth), if
necessary
Vocabulary
Find the unit price. Round to the nearest cent.
$60.00 for 12 books
1) Write as a rate in fraction form
with the price in the numerator
2) Divide
3) Rewrite as a phrase or as a fraction
with labels
$60
12 
$5
$5 per book
$5

Unit Price
1) $46.20 for 6 shirts
3) $1.47 for 1.5 lb broccoli
Examples
2) $14.28 for 12 lb of turkey
4) $0.60 for 12 oz of rolls
12 bananas for $1.80 or 15 bananas for $2
1) Find the unit price for each item.
$1.80
12 
$2
15 
2) Compare. The better buy is the
cheaper (lesser) amount.
$0.15

$0.13

15 bananas for $2 is the better buy.
Which is the better buy?
1) 3 tacos for $3.50 or 4 tacos for $5.00
2) 12 books for $119.40 or 6 books for $53.34
Examples
8-7: Make a List
{
IWBAT solve problems by making an organized
list
8-8: Similar Figures
{
IWBAT use proportions to solve problems
involving similar figures

Similar Figures – Figures that have the same
shape but not necessarily the same size.
Vocabulary
8-9: Scale Drawings
{
IWBAT interpret scale drawings.


Scale Drawing – a reduction or enlargement of
an actual object.
Scale – a ratio that compares a measure on a
drawing with the actual measure.
Vocabulary
8-10: Using Maps
{
IWBAT use map scales and proportions to find
actual distances

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