Unit 1Unit 1

Ratios and Unit Ratios and Unit RatesRates

Unit 1Unit 1

Ratios and Unit Ratios and Unit RatesRates

How do we use ratios How do we use ratios and unit rates to and unit rates to

solve real-world math solve real-world math problems?problems?

How do we use ratios How do we use ratios and unit rates to and unit rates to

solve real-world math solve real-world math problems?problems?

•Ratio• Rates

CCSS: 6.RP.2; 3b

Ratio• Compares two numbers or

quantities by division

• part to part• part to whole

• whole to part

Ratio•Word form 2 to 5•Ratio form 2:5•Fraction form 2 5

Equivalent Ratios

•Write the ratio as a fraction •Mult or div the numerator and denominator by the same nonzero number

•Write the result as a fraction

Equivalent Ratios•Use cross products to determine

if ratios (fractions) are equivalent

Equivalent Ratios•Proportions – two ratios are equivalent

•Two ratios form a proportion if their cross products are equal

Proportion“equal fractions”

• Words 3 : 12 = 5 : 20

• fraction 3 = 5 12 20

cross products 3 x 20 = 12 x 5

60 = 60

Ratioproportion

Percent “%”

a ratio that compares a number to 100.

Ratio as a percent of a

number

• Use a proportion part = % whole 100

• in words is = % of 100

•Find the part….What is?

•Ratio• Rates

CCSS: 6.RP.2; 3b

Rate as a percent

• Use a proportion part = % whole 100

• in words is = % of 100

• Find the part of 100….What %?

Rates•A ratio that compares two quantities

with different units of measure

Unit rate Unit price “$”

•Unit rate• Unit $

unit cost or unit price

CCSS: 6.RP.2; 3b

Unit Rate•Compare two quantities with different units of measure

•Has 1 unit as its second term, or denominator

Unit Rate 40 breaths in 1 minute 55 miles per hour 32 miles on 1 gallon 80 words per minute

Unit Cost (price)

$ 5.50 per hour $ 1.75 per lb $ 14.00 for 1 book $ 4.00 for 1 ticket

Key Concepts• Ratios• Unit Rates• Proportional Relationships• Percent and percentage problems• Measurement conversions (metric and

standard)• Ordered pairs in all quadrants of the

coordinate plane

Vocabulary• Comparison• Equivalent• Fractional

representation• Per• Rate• Unit price• Unit rate• Equivalent ratio

• Percent• Rate• Transform units• quadrants• coordinate plane• coordinates• Absolute value• Origin