Unit 1 Ratios and Unit Rates Unit 1 Ratios and Unit Rates

How do we use ratios and unit rates to solve real-world math 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 = cross products 3 x 20 = 12 x 5 60 = 60

Ratio proportion 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 $ 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