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Chapter 7: Lesson 3 Multi-Step Equations with Fractions and Decimals

Chapter 7: Lesson 3 Multi-Step Equations with Fractions and Decimals. Pre-Algebra-6 May 29, 2012. Warm Up:. y = -7. -9 = 3(y + 4) 5(t – 8) = 10 x + 7 – 3x = 7. t = 10. x = 0. Coefficients of Variables. A coefficient is the number, fraction, or decimal INFRONT OF a variable .

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Chapter 7: Lesson 3 Multi-Step Equations with Fractions and Decimals

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  1. Chapter 7: Lesson 3Multi-Step Equations with Fractions and Decimals Pre-Algebra-6 May 29, 2012

  2. Warm Up: y = -7 • -9 = 3(y + 4) • 5(t – 8) = 10 • x + 7 – 3x = 7 t = 10 x = 0

  3. Coefficients of Variables • A coefficient is the number, fraction, or decimal INFRONT OFa variable. • When the coefficient is a fraction, use the RECIPROCAL of that fraction to solve the equation. • Remember, always MULTIPLY by the reciprocal. • Solve: (4/5)x = 12 This is a Constant This is a Coefficient

  4. Multi-Step Equations & Fractions/Coefficients • Still follow the rules of any Multi-Step Equation, UNDO the Equation, SADMEP! • Get all of the constants on one side, leaving the variables and coefficients on the other side. (coefficient)(variable) = constant • Then get rid of the coefficient by undoing it. • For example: multiplying by the reciprocal.

  5. Like This • Solve (2/3)n – 6 = 22 (2/3)n – 6 + 6 = 22 + 6 (Add. Prop. of Eq.) (3/2) (2/3)n = 28 (3/2) (Multiply by the Reciprocal) (6/6)n = (28 • 3)/2 (Simplify) 1n = 84/2 (Simplify) n = 42 (Solved)

  6. Try These: Undo (SADMEP) 50 = k • (-7/10)k + 14 = - 21 • (2/3)(m – 6) = 3 (21/2) or (10 ½) = m

  7. Real World Problem • A student has two test scores of 93 and 80. Solve the equation (93+80+t)/3 = 90 to find what the student would have to score on a third test to average 90.

  8. Step By Step • (93 + 80 + t) = 90 Equation • 3 • (3) (93 + 80 + t) = 90 (3) Multi. Prop. of Eq. • 3 • 93 + 80 + t = 270 Simplify • 173 + t = 270 Simplify • 173 – 173 + t = 270 – 173 Sub. Prop. of Eq. • t = 97 Simplify The student would have to score 97 on a third test to average 90.

  9. Try These -38 = x • - 12 + x = 13 2 • 4 (a + 6) = 2 7 -5/2, or (–2 ½) = a

  10. Making Fractions Easier • Use the LEAST COMMON MULTIPLE (LCM) of the Denominator to clear the equation of fractions. • 2 x + 2 = 3 Find a LCM for 5 and 4. • 5 4 • 20 (2/5 x + 2) = 20 (3/4) Multi. Prop. of Equality • 40/5 x + 40 = 60/4 Simplify • 8x + 40 = 15 Simplify Again • 8x + 40 – 40 = 15 – 40 Sub. Prop. of Equality • 8x = - 25 Div. Prop of Equality • x = -25/8 or (–3 1/8) Solution

  11. Try These 1/3 = y • -(5/8)y + y = 1/8 • (1/3)b – 1 = 5/6 11/2, or 5 ½ = b

  12. Working with Decimals • If you have decimals as coefficients, you can work with them two ways. • Method 1: Just working with the decimal as a decimal. • Method 2: Clear out the decimal by multiplying everything by powers 10.

  13. Method 1: Dismal Decimals • Method 1: Just work with them. • 0.035m + 9.95 = 12.75 • - 9.95 -9.95 Sub. Prop. of Eq. • 0.035m = 2.8 • 0.035 0.035 Div. Prop. of Eq. • m = 80 • Just have to do long division with decimals. • Not too bad…BUT, Method 2, might be easier.

  14. Method 2: Clear the Decimals • Use the decimal with the greatest number of decimal places to decide what power of 10 to use. • So if the greatest decimal is 0.0001, multiply everything by 10,000. 0.035m + 9.95 = 12.75 1,000 (0.035m + 9.95) = 12.75 (1,000) 35m + 9,950 – 9,950 = 12,750 – 9,950 35m/35 = 2,800/35 m = 80

  15. Try This One With Either Method • -0.8k – 3.1 = -8.3 • Answer, k = 6.5

  16. Assignment #54 • Page 348-349: 11-35 all.

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