Transcript Chapter 8x
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
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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
𝑛
=
3 21
1) Simplify vertically and/or
horizontally, if possible
2 𝑛
=
1 7
2) Cross-multiply
𝑛 = 14
3) Solve for 𝑛, if needed
Find the missing number
1)
6
9
8
=𝑛
2)
9
15
𝑛
= 10
3)
8.5
3.2
=
𝑛
8
5) Three boxes of cereal cost $10.50. What does one box cost?
Examples
4)
2.6
𝑛
4
= 4.8
8-4: Too Much or Too
Little Information
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IWBAT determine which information is missing
and identify extraneous information in problems.
8-5: Rates
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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 𝑚𝑖𝑙𝑒𝑠
90 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
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 𝑚𝑖𝑙𝑒𝑠
𝑚𝑖𝑛𝑢𝑡𝑒
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 𝑏𝑜𝑜𝑘𝑠
$5
$5 per book
$5
𝑏𝑜𝑜𝑘
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 𝑏𝑎𝑛𝑎𝑛𝑎𝑠
$2
15 𝑏𝑎𝑛𝑎𝑛𝑎𝑠
2) Compare. The better buy is the
cheaper (lesser) amount.
$0.15
𝑏𝑎𝑛𝑎𝑛𝑎
$0.13
𝑏𝑎𝑛𝑎𝑛𝑎
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
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IWBAT solve problems by making an organized
list
8-8: Similar Figures
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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
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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
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IWBAT use map scales and proportions to find
actual distances