Ratios and Unit Rates Lesson
Learn to express ratios as fractions, simplify rates, and find unit rates. Practice converting units and calculating costs per pound in shopping scenarios.
Ratios and Unit Rates Lesson
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Transparency 1 Click the mouse button or press the Space Bar to display the answers.
Example 1-4b Objective Express ratios as fractions in simplest form and determine unit rates
Example 1-4b Vocabulary Ratio A comparison of two numbers by division
Example 1-4b Vocabulary Rate A comparison of two quantities with different types of units
Example 1-4b Vocabulary Unit Rate When a rate is simplified so it has a denominator of 1
Example 1-4b Vocabulary Math Symbols Approximately equal to
Lesson 1 Contents Example 1Write Ratios in Simplest Form Example 2Write Ratios in Simplest Form Example 3Find a Unit Rate Example 4Compare Unit Rates
Answer:The ratio = Example 1-1a Express 12 blue marbles out of 18 marbles in simplest form. Write rate as fraction Begin with numerator Put fraction bar Write denominator Put fraction in calculator and simplify 1/4
Example 1-1b Express 5 blue marbles out of 20 marbles in simplest form. Answer: Ratio = 1/4
Example 1-2a Express 10 inches to 2 feet in simplest form. Write rate as fraction Must have same unit in numerator as in denominator Convert to the smaller unit which is inches Convert 2 feet to 24 inches. Cancel like units 2/4
Answer: The ratio = Example 1-2a Express 10 inches to 2 feet in simplest form. Put fraction in calculator and simplify 2/4
Example 1-2b Express 14 inches to 2 feet in simplest form. Answer: 2/4
Example 1-3a READINGYi-Mei reads 141 pages in 3 hours. How many pages does she read per hour? Write rate as fraction Find a unit rate Divide the numerator by the denominator 141 pages ÷ 3 3 hours ÷ 3 Divide the denominator by the denominator 47 pages 1 hour Answer: Yi-Mei reads an average of 47 pages per hour 3/4
Example 1-3b 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
Example 1-4a SHOPPINGAlex 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? Write a rate for each item Almonds: Find unit rates of each item Jellybeans: 4/4
Example 1-4a SHOPPINGAlex 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? ÷ 2 Divide numerator by denominator Almonds: ÷ 2 Divide denominator by denominator $6.25 1 pound 4/4
Example 1-4a SHOPPINGAlex 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? ÷ 5 Divide numerator by denominator Jellybeans: ÷ 5 Divide denominator by denominator $4.77 1 pound 4/4
Example 1-4a Which item costs less per pound? By how much? Since the denominators are both the same (1 pound) then compare the numerators Almonds: Jellybeans: Since the denominators are both the same (1 pound) then subtract numerators Jellybeans cost less (Almonds) $6.25 – $4.77 (Jellybeans) $1.48 Answer: Jellybeans cost $1.48 per pound less than almonds 4/4
Example 1-4b * SHOPPINGCameron 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 4/4
End of Lesson 1 Assignment