The Multiplication Principle of Equality

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Presentation transcript:

The Multiplication Principle of Equality 2.3b The Multiplication Principle of Equality 3. Use the multiplication principle to clear fractions and decimals from equations.

Review: Terms Three terms Three terms Three terms

Review: Terms Four terms Four terms Four terms

Review 3 1 2 1

Clearing Fractions Distributive Property 1 1 1 Equivalent equation but no fractions!!! Multiply EVERY TERM by the LCD, even if the term does not contain a fraction. Expression. Can’t clear the fractions. Only works with EQUATIONS!

Clearing Fractions To Solve Linear Equations 1. Clear the fractions. 2. Simplify both sides of the equation as needed. a. Distribute to clear parentheses. b. Combine like terms. 3. Use the addition principle so that all variable terms are on one side of the equation. 4. Use the addition principle so that all constants are on the other side. 5. Use the multiplication principle to isolate the variable.

Clearing Fractions 1. Clear fractions. 2. Simplify 3. Move the variable terms. 4. Move the constants. 5. Isolate the variable. LCD: 18 Terms: 3 3 1 2 1 Goal: Denominators = 1 Take the time to rewrite!

Clearing Fractions 1. Clear fractions. 2. Simplify 3. Move the variable terms. 4. Move the constants. 5. Isolate the variable. LCD: 12 Terms: 4 4 1 3 1 2 1

Clearing Fractions 1. Clear fractions. 2. Simplify 3. Move the variable terms. 4. Move the constants. 5. Isolate the variable. LCD: 10 Terms: 3 2 1 1 2 1

Decimals Decimals are another way to write fractions!

Multiplying Powers of 10 Move decimal point one place. Move decimal point two places. Count the number of zeros and move the decimal that many places.

Clearing Decimals 1. Clear fractions. 2. Simplify 3. Move the variable terms. 4. Move the constants. 5. Isolate the variable. LCD: 100 Terms: 3

Clearing Decimals 1 1. Clear fractions. 2. Simplify 3. Move the variable terms. 4. Move the constants. 5. Isolate the variable. 1 LCD: 10 Terms: 4 If the problem starts with decimals, leave the answer in decimal form.

Solve. 0.8 – 4(a – 1) = 0.2 + 3(4 – a) a)  10 b) 7.4 c) 8.6 d) 20.6 2.3

Solve. 0.8 – 4(a – 1) = 0.2 + 3(4 – a) a)  10 b) 7.4 c) 8.6 d) 20.6 2.3