Equivalent Ratios

Write each rate as a fraction. Then find its unit rate. Use Unit Rates Determine if 20 rolls for $5 and 48 rolls for $12 are equivalent rates. Explain your reasoning. Write each rate as a fraction. Then find its unit rate. ÷5 ÷12 = 20 rolls $5 __________ 4 rolls $1 _________ = __________ 48 rolls $12 4 rolls $1 _________ ÷5 ÷12 Answer: Since the rates have the same unit rate, , they are equivalent. 4 rolls $1 _______ Example 1

A. Yes; they have the same unit rate, . Determine if $24 for 4 hours and $30 for 6 hours are equivalent rates. Explain your reasoning. A. Yes; they have the same unit rate, . B. Yes; they have the same unit rate, . C. Yes; they have the same unit rate, . D. No; they do not have the same unit rate. Example 1 CYP

Write each rate as a fraction. Then find its unit rate. Use Unit Rates Determine if 42 people on 7 teams and 64 people on 8 teams are equivalent rates. Explain your reasoning. Write each rate as a fraction. Then find its unit rate. ÷7 ÷8 = ____________ 42 people 7 teams ___________ 6 people 1 team = ____________ 64 people 8 teams ___________ 8 people 1 team ÷7 ÷8 Answer: Since the rates do not have the same unit rate, they are not equivalent. Example 2

A. Yes; they have the same unit rate, Determine if 90 miles in 2 hours and 135 miles in 3 hours are equivalent rates. Explain your reasoning. A. Yes; they have the same unit rate, B. Yes; they have the same unit rate, C. Yes; they have the same unit rate, D. No; they do not have the same unit rate. Example 2 CYP

Write each rate as a fraction. Then find its unit rate. Use Unit Rates FOOD You can buy 3 medium pizzas at The Pizza Place for $18 or 5 medium pizzas for $30. Are these selling rates equivalent? Explain your reasoning. Write each rate as a fraction. Then find its unit rate. ÷3 ÷5 = __________ $18 3 pizzas _________ $6 1 pizza = __________ $30 5 pizzas _________ $6 1 pizza ÷3 ÷5 Example 3

Answer: Since the unit rates are the same, , the rates are equivalent. Use Unit Rates Answer: Since the unit rates are the same, , the rates are equivalent. _______ $6 1 pizza Example 3

CARWASHING On Saturday, the tennis team washed 42 cars in 3 hours to raise money for the team. On Sunday, they washed 60 cars in 5 hours. Are these work rates equivalent? Explain your reasoning. A. Yes; since the unit rates are the same, the rates are equivalent. B. Yes; since the unit rates are the same, the rates are equivalent. C. Yes; since the unit rates are the same, the rates are equivalent. D. No; since the unit rates are not the same, the rates are not equivalent. Example 3 CYP

Use Equivalent Fractions Determine if 5 laps swum in 8 minutes and 11 laps swum in 16 minutes are equivalent rates. Explain your reasoning. Write each rate as a fraction. ×2.2 = ____________ 5 laps 8 minutes ___________ 11 laps 16 minutes ? ×2 The numerator and the denominator are not multiplied by the same number. So, the fractions are not equivalent. Example 4

Use Equivalent Fractions Answer: Since the fractions are not equivalent, the rates are not equivalent. Example 4

Determine if 4 free throws made out of 6 attempts and 8 free throws made out of 12 attempts are equivalent ratios. A. No; since is not a unit rate, the ratios are not equivalent. B. Yes; since the ratios are equivalent. C. Yes; since the fractions are equivalent. D. No; since the fractions are not equivalent, the ratios are not equivalent. Example 4 CYP

Use Equivalent Fractions Determine if 8 corrals with 56 horses and 4 corrals with 28 horses are equivalent ratios. Explain your reasoning. Write each ratio as a fraction. ÷2 = ____________ 8 corrals 56 horses ___________ 4 corrals 28 horses ? ÷2 Example 5

Use Equivalent Fractions The numerator and the denominator are divided by the same number. So, the fractions are equivalent. Answer: Since the fractions are equivalent, the ratios are equivalent. Example 5

A. Yes; since the ratios are equivalent. Determine if 15 boys out of 36 students and 5 boys out of 9 students are equivalent ratios. A. Yes; since the ratios are equivalent. B. Yes; since the fractions are equivalent. C. No; since is not a unit rate, the ratios are not equivalent. D. No; since the ratios are not equivalent. Example 5 CYP