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Solving Simple Equations and Conversions
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What are inverse operations?
The inverse operations are operations that UNDO one another Examples: Addition and Subtraction Multiplication and Division Square and Square Root Can you think of any others?
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Try some examples 5 = -9 + v Z + 8 = 0 -7n = 28 -y/7 = 35 m/2 – 7 = 14
3x + 8x – 6 = 28 1/2y – 3/4y = /4y x2 + 7 = 32
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What are inverse operations really doing?
When you use the inverse operations you are CANCELLING OUT terms to get to a desired result 5x + 3 = 18 -3 = -3 5x = 15 5 = 5 x = 3
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Let’s try a word problem…
Each book at the book store sold for the same amount. Suppose you bought 6 mysteries and 6 romance books. Then you bought a poster for $ You spent a total of $ How much did each book cost? -Create an equation that represents this word problem -Solve the equation
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SOLUTION Equation: 6b + 6b + 2.40 = 8.70 Solution: 12b + 2.40 = 8.70
-2.40 = -2.40 12b = 6.30 12 = 12 b = .525 So each book cost $0.53
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Now it is your turn!! 2c + c + 12 =78 2. y/4 + 9 = 25
Write your own word problem for the following equations: 2c + c + 12 =78 2. y/4 + 9 = 25
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How does Canceling apply to Computing Conversions?
When you compute a conversion, you cancel your units to get to the desired unit Example: How many nickels are in 2 dollars? 2 dollars = 4 quarters = 5 nickels = ? 1 dollar 1 quarter 40 NICKLES IN 2 DOLLARS
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Money Conversion So we know that 40 nickels = 2 dollars but can we figure out how many nickels are in 100 Euros? HINT: The Euro is the currency in Europe 10 dollars = 12 Euros
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Solution 1 Dollar 20 Nickels 10 Euros 12 Dollars 1 Nickel = =
SO….1 Nickel = .041 Euro
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Now it is YOUR turn Mr. Mayberry the farmer grows blackberries. He wants to trade 200 blackberries with his neighboring farmers. Mr. Apple will trade 5 apples for 40 blackberries Mr. Yellow will trade 3 lemons for 50 blackberries Mr. Slice will trade 7 oranges for 60 blackberries NOTE: 4 oranges are worth 3 apples 5 lemons are worth 9 oranges WHO SHOULD MR. MAYBERRY TRADE WITH IF HE WANTS TO GET MORE THAN 16 WHOLE APPLES?
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SOLUTION SO MR. MAYBERRY SHOULD TRADE WITH MR. APPLE AND MR. SLICE BUT NOT WITH MR. YELLOW!!
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