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• 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

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

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

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

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

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

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)