w + 5 = 20 11x + 10 = 76
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1 Course: 8 th Grade Math DETAIL LESSON PLAN Lesson 5..2 Additional Practice TSW solve equations with fractions and decimals. Big Idea How can I eliminate fractions and decimals in equations? Objective 8.EE.7b Homework Teacher Selected Bellwork Teacher Selected Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Prior Knowledge Review bellwork. Review homework. See examples of equations we ve solved to date. Introduce Lesson TODAY, we will continue to practice solving equations with fractions and decimals. Teacher Input Review the definition of an equation and display examples of equations. Briefly discuss the types of equations learned thus far. Focus in on the last two equations which have fractions and decimals. w + 5 = 20 x + 0 = 76 m + 2m 4 = 4 4x 2 2x = x 5 x 2(5x + ) = 4 2x One-Step Equations Two-Step Multi-Step Variables on One Side Multi-Step Variables on Both Sides Multi-Step with Distributive Property 4x + x 2 = 7 6 Equations with Fractions 2.x = 7.4 Equations with Decimals Review CPM Methods and Meanings on Fraction Busting (also found in textbook). Work guided practice problems. Students should work the you try problems independently. Review Methods and Meanings on Clearing Decimals. Work guided practice problems. Students should work the you try problem independently. Pass out the classwork (5 problems). Teacher should go over the answers to the classwork to ensure understanding. Assessment Observation and questioning. Closure See closing thoughts at the end of this lesson. This can be done whole group.
2 What is an Equation? A mathematical sentence with an equal sign (=). Examples: w + 5 = 20 x + 0 = 76 m + 2m 4 = 4 4x 2 2x = x 5 x 2(5x + ) = 4 2x 4x + x = x = 7.4
3 Big Idea: How can I eliminate fractions in equations? The method is called Fraction Busting! Let s review how it works: Solving Equations with Fractions Example: Solve for x x + x 5 = 2 This equation would be much easier to solve if it had no fractions. Therefore, the first goal is to find a equivalent equation that has no fraction. x + x 5 = 2 The lowest common denominator of x is 5. and x 5 To eliminate the denominators of the fractions 5 ( x + x 5 ) = 5 2 multiply both sides of the equation by the common denominator. In this example, the 5 x LCD is 5, so multiplying both sides of the equation by 5 eliminates the fractions. + 5 x 5 = 5 2 The result is an equivalent equation without 5 x + x = 0 fractions! 8 x = 0 The number used to eliminate the denominators is called a Fraction Buster. Our fraction buster in this example was 5. Now the equation looks like many you have seen before, and it can be solved the usual way. Combine like terms & Divide both sides by 8 x =. 75
4 Multi-Step Equations with Rational Coefficients Guided Practice Problems Example : Fraction Busting You Try: Solving Steps x + 2 = Original x equation Explanation 2 ( x + 2) = 2 ( x + 7) 4 2 ( x) + 2 ( 2) = 2 ( x) + 2(7) 4 4x + 24 = x + 84 x + 24 = 84 x = 60 You Try: Solve for x. You Try: Solve for x. 2x + = 4 x 2 + x 5 = 7
5 Guided Practice Problems - Continued Example 2: Fraction Busting with the Distributive Property Procedure: Distribute and then clear the fractions. Solving Steps 2 (x + 2 Original ) = (x ) 2 x + Distribute = x equation Explanation and simplify 6 ( 2 x + ) = 6(x ) Multiply both sides by the LCD ( x) + 6( ) = 6(x) 6() Distribute 2 x + 2 = 8 x 8 2 = 5x 8 20 = 5x Multiply Subtract x from both sides Add 8 to both sides 20 5 = x Divide both sides by 5 4 or = x Simplify You Try: Solve for y. 8 (y + 2) = 4 (2y + 2 ) + 2
6 Big Idea: How can I eliminate decimals in equations? Some people call it Clearing the Decimal! Let s review how it works: Solving Equations with Decimals Example: Solve for x 0. x +. 8 = 0. 24x x +.8 = 0.24x +.2 This equation would be much easier to solve if it had no decimals. Therefore, the first goal is to find a equivalent equation that has no decimals. Find the number with highest number of decimal places. To eliminate the decimals find the number 00 ( ) = 00(0.24x +.2) with the highest number of decimal places..8 and 0.24 go out to the hundredths place. So to clear the decimals from the equation we will need to multiply both sides by 00. The result is an equivalent equation without 0x + 8 = 24x + 20 decimals! Now the equation looks like many you have seen before, and it can be solved the usual way. x =
7 Guided Practice Problems - Example : Clearing the Decimals You Try: Solve for v v. 6 =
8 8 th Grade Math Name: Period: Multi-Step Equations with Rational Coefficients Follow these steps to solve each problem below: Apply the Distributive Property if necessary. Clear the fraction or decimal. Solve the equation as usual. ) Solving Steps Explanation x + 4 x = 4 Original equation 2 ( x + x) = 2( 4) 4 2 ( x) + 2 ( x) = 2(4) 4 4x + x = 48 7x = x = ) 2p 2 5 p = 6 6 ) 2 n 2 n = 5 5 4) 5 4 n + n = 6 8 5) 6n 5 n = 2 Continue
9 6) p 2 = 2 7) 2 x + x = 5 2 8) 2r + 5 r = ) 2 (2h ) = (2h + 2 ) 0) (2y + ) = 4 ( y) ) (5x ) = 2 (x + ) 5 2 2) 2. 9v 2v =. 8 ) 0. 5a + = 2. 8a ) = (m + ) 5) x =. 2 +.
10 Multi-Step Equations with Rational Coefficients Answer Key Guided Practice Problems Example : Fraction Busting You Try: Solving Steps x + 2 = 4 x + 7 Original equation Explanation 2 ( x + 2) = 2 ( 4 x + 7) Multiply both sides by the LCD ( x) + 2 ( 2) = 2 ( 4 x) + 2(7) Distribute 4x + 24 = x + 84 x + 24 = 84 x = 60 Multiply Subtract x from both sides Subtract 24 from both sides You Try: Solve for x. You Try: Solve for x. 2x + = x 2 + x 5 = 7 {4} {0}
11 Guided Practice Problems - Continued Example 2: Fraction Busting with the Distributive Property Procedure: Distribute and then clear the fractions. Solving Steps 2 (x + 2 Original ) = (x ) 2 x + Distribute = x equation Explanation and simplify 6 ( 2 x + ) = 6(x ) Multiply both sides by the LCD ( x) + 6( ) = 6(x) 6() Distribute 2 x + 2 = 8 x 8 2 = 5x 8 20 = 5x Multiply Subtract x from both sides Add 8 to both sides 20 5 = x Divide both sides by 5 4 or = x Simplify You Try: Solve for y. 8 (y + 2) = 4 (2y + 2 ) + 2 y =
12 Guided Practice Problems - Example : Clearing the Decimals You Try: Solve for v v. 6 = v = 8
13 8 th Grade Math Answer Key Multi-Step Equations with Rational Coefficients Follow these steps to solve each problem below: Apply the Distributive Property if necessary. Clear the fraction or decimal. Solve the equation as usual. ) 2) 2p 2 5 p = 6 6 ) 2 n 2 n = 5 5 {} {} 4) 5 4 n + n = 6 8 5) 6n 5 n = 2 {2} { } Continue
14 6) p 2 = 2 7) 2 x + x = 5 2 { 4 } {7 4 or 4 } 8) 2r + 5 r = ) 2 (2h ) = (2h + 2 ) { 6 } {2} 0) (2y + ) = 4 ( y) ) (5x ) = 2 (x + ) 5 2 { 4 } {4 5 = 2 5 } 2) 2. 9v 2v =. 8 ) 0. 5a + = 2. 8a + 4. {2} {} 4) = (m + ) 5) x = {. 4} {2. 6}
15 Closing Thoughts Let s recap what we ve learn about Fraction Busting. See if you can use the word bank to fill in the blanks! The words in the bank may be used more than once! m + 2m = 9. To make the above problem easier to solve, I need to the fractions. 2. We can use a method called to accomplish this.. We start by looking at the denominators of the fractions. The denominators are and. 4. What common multiple can I use to eliminate these denominators? Drag and Drop Fraction Busting - equivalent - eliminate - m + 8m = - Buster 5. This common multiple is called the Fraction. 6. Now that I know what the fraction buster is, I can multiply both sides of the equation by to create an problem without the fractions! 7. My new equation is:
16 m + 2m = 9 Answer Key. To make the above problem easier to solve, I need to eliminate the fractions. 2. We can use a method called Fraction Busting to accomplish this.. We start by looking at the denominators of the fractions. The denominators are and What common multiple can I use to eliminate these denominators? 9 Drag and Drop Fraction Busting - equivalent - eliminate - m + 8m = - Buster 5. This common multiple is called the Fraction Buster. 6. Now that I know what the fraction buster is, I can multiply both sides of the equation by 9 to create an equivalent problem without the fractions! 7. My new equation is: m + 8m =
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