1. Rational Numbers & Equations Lesson 3-5

2. Rational Numbers & Equations When given an equation with a fraction… a)Solve by multiplying by the reciprocal b)Solve by canceling fractions using the LCD (lowest common denominator)

3. Solving by a fraction To “solve” with a fraction  multiply by the reciprocal 2 m = 200 3 3. 2 m = 200. 3 2 3 2 m = 100 3 m = 300  given  Multiply by reciprocal [Check for cross reducing]  (Fractions cancelled out) Solve!

4. Solving by a fraction 2 y = 8 5 5. 2 y = 8. 5 2 5 2 y = 4 5 y = 20 - b = 2 8 -8 - b = 2 -8 8 b = 2 -8 b = -16

5. Solving a fraction equation To “solve” with fractions in the problem  multiply all terms by the LCD 1 x + 3 x = 5 2 4 (4) 1 x + (4) 3 x = 5 (4) 2 4 2x + 3x = 20 5x = 20 x = 4  given  Multiply all equation terms by LCD [Cross reduce to cancel denominators]  New equation  Solve!

6. Solving a fraction equation y + y = -4 8 12 (24) 2y + (24) 3y = -4 (24) 8 12 6y + 6y = -96 12y = -96 y = -8

7. Practice… Solve… a)_ 3 f = 6 4 b)-2 = 4c 9 c) 2y + y = 22 3 4 d) 3n – 2 = -7 5

8. Homework p. 131 #14-17, 19-22, 31-33