DO NOW. OBJECTIVE : SWBAT Solve problems involving proportional relationships Convert between measurement systems using unit rates and using proportions.

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