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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

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Unit 1 Ratios and Unit Rates

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  1. Unit 1Ratios and Unit Rates

  2. How do we use ratios and unit rates to solve real-world math problems?

  3. Ratio • Rates CCSS: 6.RP.2; 3b

  4. Ratio • Compares two numbers or quantities by division • part to part • part to whole • whole to part

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

  6. 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

  7. Equivalent Ratios • Use cross products to determine if ratios (fractions) are equivalent

  8. Equivalent Ratios • Proportions – two ratios are equivalent • Two ratios form a proportion if their cross products are equal

  9. Proportion“equal fractions” • Words 3 : 12 = 5 : 20 • fraction3 = 5 12 20cross products 3 x 20 = 12 x 5 60 = 60

  10. Ratioproportion Percent “%” a ratio that compares a number to 100.

  11. Ratioas a percent of a number • Use a proportion part = % whole 100 • in words is = % of 100 • Find the part….What is?

  12. Ratio • Rates CCSS: 6.RP.2; 3b

  13. Rateas a percent • Use a proportion part = % whole 100 • in words is = % of 100 • Find the part of 100….What %?

  14. Rates • A ratio that compares two quantities with different units of measure Unit rateUnit price“$”

  15. Unit rate • Unit $unit cost or unit price CCSS: 6.RP.2; 3b

  16. Unit Rate • Compare two quantities with different units of measure • Has 1 unit as its second term, or denominator

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

  18. Unit Cost (price) $ 5.50 per hour $ 1.75 per lb $ 14.00 for 1 book $ 4.00 for 1 ticket

  19. 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

  20. Vocabulary • Comparison • Equivalent • Fractional representation • Per • Rate • Unit price • Unit rate • Equivalent ratio • Percent • Rate • Transform units • quadrants • coordinate plane • coordinates • Absolute value • Origin

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