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Rational Equations

Rational Equations. Objective: Students will apply the principals of rational numbers to solving equations. Warm-up Times tables and Squares 12-32. Rational Properties. LCD is the lowest common denominator The LCD is the LCM of the denominators

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Rational Equations

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  1. Rational Equations • Objective: Students will apply the principals of rational numbers to solving equations. • Warm-up Times tables and Squares 12-32

  2. Rational Properties • LCD is the lowest common denominator • The LCD is the LCM of the denominators • The least common multiple can be found by listing them for each denominator. • 1/4 4,8,12,16,20,24,28.32 • 3/7 7, 14, 21, 28, 35 • 1/4 = 7/28 3/7 = 12/28 • 1/4 + 3/7 = 7/28 + 12/28 = 19/28

  3. Rational Properties • ½ x 50 = 25 • ½ x ½ = ¼ • When multiplying fractions multiply numerator by numerator and denominator by denominator • 2/7 x 3/4 = 2 x 3/ 7 x 4 = 6/28 = 3/14 • ¾ of 20 = 15 ¾ of 5/8 = 15/32

  4. Rational Properties • Consider x/2 + 3/5 = 7/2 • Find the LCD • It’s 10 • OK 5x/10 + 6/10 = 35/10 • BETTER 5x + 6 = 35 • The first “OK” attempt used 10 as an LCD • The second multiplied by sides of the equation by the LCD • Get rid of the fractions in all rational equations first

  5. Rational Properties • Consider 0.03x + 11.34 = 13.2 • Find the LCD? • It’s 100 HUH! • Multiply everything by 100 • Now you have x + 1134 = 1320

  6. Rational Properties • Consider 3/x + 12/x +1 = 1/ x • Get rid of the fractions first • LCD = x (x + 1) Multiply both sides by LCD • Results 3(x + 1) + 12x = x + 1 • Distribute 3x + 3 + 12x = x + 1 • CLT 15x + 3 = x + 1 • Next 14x = - 2 • Finally x = -1/7

  7. Rational Properties • Consider 2x+1/3x+1 = 4/3 • Get rid of the fractions first • LCD = 3(3x + 1) = 9x + 3 • Results 3(2x + 1) = 4 (3x + 1) • Distribute 6x + 3 = 12 x + 4 • Then -6x = 1 • Then x = -1/6

  8. Rational Properties • Go to TCA rational equations • One time for practice Next time for the money. • Remember idiots think the answers are: a, b, c , d , a, c, b, a, d • Grading is easy, get the benefit of honest work. You cheat (yourself)

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