Solving Simple Equations and Conversions

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Presentation transcript:

Solving Simple Equations and Conversions

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?

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 = 24 + 3/4y x2 + 7 = 32

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

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 $2.40. You spent a total of $8.70. How much did each book cost? -Create an equation that represents this word problem -Solve the equation

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

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

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

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

Solution 1 Dollar 20 Nickels 10 Euros 12 Dollars 1 Nickel = = SO….1 Nickel = .041 Euro

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?

SOLUTION SO MR. MAYBERRY SHOULD TRADE WITH MR. APPLE AND MR. SLICE BUT NOT WITH MR. YELLOW!!