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Solving Multi-Step Equations with Fractions and Decimals

In this lesson, we advance our skills in solving multi-step equations by incorporating fractions and decimals. We will tackle equations with two steps, beginning with combining like terms and applying the distributive property. An example walks us through the process: first adding a number to both sides, then multiplying both sides by a fraction. We'll be addressing challenges, such as distributing fractions and clearing fractions using the least common multiple. Practice problems will reinforce these concepts, preparing you for an upcoming quiz.

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Solving Multi-Step Equations with Fractions and Decimals

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  1. 1-21-11 • Bellwork #40 • HW, red pen, pencil, book on desk.

  2. Multi-Step equations with fractions and decimals Lesson 7-3 p.345

  3. Multi-step equations • We have added to the level of difficulty by solving equations with 2 steps, by combining like terms first, and by using the distributive property. • Now we increase the difficulty again by solving equations with fractions and decimals.

  4. Example • For example: Our steps are the same in this problem. First we add six to both sides, then we multiply both sides by 3/2 and then solve. Let’s try it.

  5. Let’s try +6 +6

  6. Another example • Sometimes we have to distribute the fraction like this:

  7. Try This • 1.2n + 3.4 = 10 • (a + 6) = 2

  8. Try This • 1.2n + 3.4 = 10 n = 5.5 • (a + 6) = 2

  9. Try This • 1.2n + 3.4 = 10 n = 5.5 • (a + 6) = 2 a = -5/2

  10. Another example First add 8 to both sides +8 +8 Next multiply both sides by 2 (2) (2) Subtract 14 from both sides and solve. -14 -14 N = 22

  11. Try This

  12. Try This X = 38

  13. Try This X = -38 R = 97

  14. Clear the equation of fractions • Multiply each side by the LCM to get rid of the fraction or fractions. • Study example #3 on p.346

  15. Agenda 1-21-10 • PA#4 • P.348 #14-22

  16. 1-24-11 • Please start Bellwork Quiz • HW, red pen, pencil on desk.

  17. Agenda 1-24-11 • PA#5 • Workbook pages: • p.57 #5-17 odd, • p. 58 #1-13 odd, and • p.59 #5-15 odd • Show work in spiral notebook • Quiz tomorrow on Lessons 7-1, 7-2, and 7-3.

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