Lesson 2: 7-2 Adding and Subtracting Rational Expressions

1. What is the lowest common denominator for 1/2, 3/8, and 3/4?
2. To add the three fractions together, what would the equivalent fractions be with the common denominator?
3. Add the fractions.
4. What is the next step?

LCM
LCD

A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, and multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

SAT questions related to rational functions: 1-3-13, 6-3-12

When rational expressions are given the same denominators in preparation for addition or subtraction, they are equivalent to the original expressions. Multiplying a rational expression by a form of 1 such as 6x/6x or (y-3)/(y-3) does not change the value of the expression.

As a fire engine moves toward a person, the pitch of the siren sounds higher to that person than it would if the fire engine were at rest. This is because the sound waves are compressed closer together, referred to as the Doppler effect. The Doppler effect can be represented by a rational expression.

Have students discuss the differences between procedures for adding and multiplying fractions. It is important that they see why common denominators are required for addition but not for multiplication.

Have students work with a partner, one in the role of a coach, the other in the role of an athlete. The athlete works a problem, using steps and explaining the thinking while the coach listens and watches for errors, correcting as necessary. Then the partners exchange roles.

McGraw Hill resources

McGraw Hill resources