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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
1/4
Begin with numerator
Put fraction bar
Write denominator
Express 5 blue marbles out of 20 marbles in simplest form.
Answer: Ratio =
1/4
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
3/4
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
3/4
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?
4/4
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