Ratios and Rates more fractions Where Have We

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Ratios and Rates more fractions

Ratios and Rates more fractions

Where Have We Seen Ratios Before? 4 girls to every 3 boys = 4:

Where Have We Seen Ratios Before? 4 girls to every 3 boys = 4: 3 2 students to each book = 2: 1 7 miles/ 1 gallon = 7: 1 6 miles traveled each hour = 6: 1 17 liters of oil spill every 10 minutes = 17: 10

Ratios: relationship that compares quantities/amounts • Can be written three ways a to b

Ratios: relationship that compares quantities/amounts • Can be written three ways a to b a: b all ways are read as “a to b” • Are written in simplest form 5: 10 1: 2 • Two types of Ratios: Part to Part Ratios and Part to Whole Ratios

Part to Part Ratios What is the ratio of shaded parts to unshaded parts?

Part to Part Ratios What is the ratio of shaded parts to unshaded parts? 5 shaded to 3 unshaded 5 : 3 5 3

Part to Whole Ratios What is the ratio of shaded parts to the whole?

Part to Whole Ratios What is the ratio of shaded parts to the whole? 6 shaded to 8 parts total 6 : 8 6 8 3 to 4 3 : 4 3 4

Constant vs Random Ratio Relationships • Constant ratios: remain the same ex. For every

Constant vs Random Ratio Relationships • Constant ratios: remain the same ex. For every year there will be 12 months 1 year 1: 12 2 years 2: 24 Simplified 3 Years 3: 36 1: 12 • Random ratios: can change independently ex. For every male teacher there are 4 female teachers 1 : 4 1 : 5 *new female teacher hired 1 : 2 *female teachers quit No Constant Relationship

Equivalent Ratios • Ratios that look different but have the same value (like equivalent

Equivalent Ratios • Ratios that look different but have the same value (like equivalent fractions) Ex: 1: 4 = 2: 8 Ex: 5 35 = 7 49 When Fractions are equal the ratio relationships they represent are equivalent

To Determine if Ratios are Equivalent

To Determine if Ratios are Equivalent

To Determine if Ratios are Equivalent

To Determine if Ratios are Equivalent

Equivalent Ratio Practice Ex 1: 3 7 4 8 Ex 2: 10 2 50

Equivalent Ratio Practice Ex 1: 3 7 4 8 Ex 2: 10 2 50 10 Ex 3: Are these ratios equivalent? Ex 5: 2 9 4 18 Ex 4: 6 12 11 22 5 15 8 40 Ex 6: 20 2 10 1

Ratio Tables Use a Ratio Table to find equivalent ratios: ex: There are 4

Ratio Tables Use a Ratio Table to find equivalent ratios: ex: There are 4 dogs to 10 total pets at the pet shop dogs 4 8 12 20 40 pets 10 20 30 50 100 . Graph the relationship: . .

What is a Rate? • A rate is a ratio that compares two different

What is a Rate? • A rate is a ratio that compares two different units. rate ex: Dollars per Pound $5: 3 pounds apples ex: Miles per Gallon 30 miles : 2 gallons • A unit rate is a rate where one of the units is = 1. unit rate ex: What is the unit rate for 30 miles to 2 gallons? 30 miles = 15 miles *for every 1 gallon used, you travel 15 miles 2 gallons = 1 gallon