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Objective

Express ratios as fractions in simplest form and determine unit rates

Vocabulary

Ratio

A comparison of two numbers by division

Vocabulary

Rate

A comparison of two quantities with different types of units

Vocabulary

Unit Rate

When a rate is simplified so it has a denominator of 1

Vocabulary

Math Symbols

Approximately equal to

Example 1 Write Ratios in Simplest Form

Example 2 Write Ratios in Simplest Form

Example 3 Find a Unit Rate

Example 4 Compare Unit Rates

Express 12 blue marbles out of 18 marbles in simplest form.

Answer: The ratio =

Write rate as fraction

Put fraction in calculator and simplify

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Begin with numerator

Put fraction bar

Write denominator

Express 5 blue marbles out of 20 marbles in simplest form.

Answer: Ratio =

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Express 10 inches to 2 feet in simplest form.

Write rate as fraction

Cancel like units

2/4

Must have same unit in numerator as in denominator

Convert 2 feet to 24 inches.

Convert to the smaller unit which is inches

Express 10 inches to 2 feet in simplest form.

Answer: The ratio =

2/4

Put fraction in calculator and simplify

Express 14 inches to 2 feet in simplest form.

Answer:

2/4

READING Yi-Mei reads 141 pages in 3 hours. How many pages does she read per hour?

Answer: Yi-Mei reads an average of 47 pages per hour

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Write rate as fraction

Find a unit rate

Divide the numerator by the denominator

141 pages ÷ 3

47 pagesDivide the denominator by the denominator

3 hours ÷ 3

1 hour

TRAVEL On a trip from Columbus, Ohio, to Myrtle Beach, South Carolina, Lee drove 864 miles in 14 hours. What was Lee’s average speed in miles per hour?

Answer: 61.71 miles per hour

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SHOPPING Alex spends $12.50 for 2 pounds of almonds and $23.85 for 5 pounds of jellybeans. Which item costs less per pound? By how much?

Almonds:

Jellybeans:

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Write a rate for each item

Find unit rates of each item

SHOPPING Alex spends $12.50 for 2 pounds of almonds and $23.85 for 5 pounds of jellybeans. Which item costs less per pound? By how much?

Almonds: Divide numerator by denominator

4/4

÷ 2

$6.25Divide denominator by denominator

÷ 2

1 pound

SHOPPING Alex spends $12.50 for 2 pounds of almonds and $23.85 for 5 pounds of jellybeans. Which item costs less per pound? By how much?

Divide numerator by denominator

4/4

$4.77Divide denominator by denominator

1 pound

Jellybeans:÷ 5

÷ 5

Answer: Jellybeans cost $1.48 per pound less than almonds

Almonds:

Jellybeans:

(Almonds) $6.25 – $4.77 (Jellybeans)

Which item costs less per pound?

By how much?

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Since the denominators are both the same (1 pound) then compare the numerators

Jellybeans cost less

Since the denominators are both the same (1 pound) then subtract numerators

$1.48

SHOPPING Cameron spends $22.50 for 2 pounds of macadamia nuts and $31.05 for 3 pounds of cashews. Which item costs less per pound? By how much?

Answer: Cashews cost $0.90 less than macadamia nuts

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Assignment

Lesson 4:1 Ratios & Rates 10 - 30 All