do now. objective : swbat solve problems involving proportional relationships convert between...
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DO NOW
OBJECTIVE : SWBAT
• Solve problems involving proportional relationships
• Convert between measurement systems using unit rates and using proportions
Answers Questions on Page 87
Vocabulary Review
• A ratio is a comparison of two quantities by division.̶. 17 out of 20 students, or
• A rate is a special type of ratio comparing two quantities with different units.– Driving 120 miles in 2 hours, or
• A unit rate is a rate that is simplified so that it has a denominator of 1 unit. – Driving 120 miles in 2 hours, or
20
17
hours 2
miles 120
hour 1
miles 60
hours 2
miles 120
Example :The price of three different bags of
cat food are shown in the table to the right. Which bag has the lowest price per pound?
pound
priceWrite a verbal model of what you are comparing.
lb 1
$1.38
3.5 3.5
3.5 $4.83
For the 3.5 lb bag,
The 7 pound bag is the least expensive at $1.35 per pound
Cat Food PricesSize of bag
(lbs)Price
($)3.5 4.837 9.45
20 27.20
lb 1
$1.35
7 7
7 $9.45
For the 7 lb bag,
lb 1
$1.36
20 20
20 $27.20
For the 20 lb bag,
NOW Try page 88 #25 to 31
Think Pair Share-shoulder partners
Properties of a proportion?
4
6
2
3
2x6=12 3x4 = 12
3x4 = 2x6
Cross Product Property
* Using Cross Products
Review: How to Solve the Proportion
k17 = 20
68 Start with the variable.
=68k 17(20)Simplify.
68k = 340Now we have an equation. To get the k by itself, divide both sides by 68.
68 68k = 5
Ex: Solve the proportion 6
2n34
If the proportion is to be true, the cross products must be equal find the cross product equation:
62n
34 24 = 3n – 6
24 = 3(n – 2)
30 = 3n
10 = n
Check:
6210
34
68
34
x 2
x 2
NOW Try page 88 #32 to 45
Think Pair Share-shoulder partners
Summary
• How do we use proportions to solve problems?
Homework
• Page 84 # 6 to 8 and Page 86 #4 and 5