Algebra 1 Section 13.2

Multiplying Fractions The basic rule is to place the product of the numerators over the product of the denominators. You can multiply first, and then cancel. It is usually easier to cancel first, and then multiply.

Example 1 1 3 5 9 27 40 • = 3 8 1 8

Multiplying Rational Expressions Multiplication of rational expressions is done in the same way as multiplication of rational numbers. As with rational numbers, it is best to cancel first.

Example 2 1 c 5 3a2c2 2b 10a 9bc • = 5a3c 3b2 1 3 1 If b = 0 or c = 0 in the original expression, this would be undefined. We will assume that no denominator of a rational expression has a value of zero.

Multiplying Rational Expressions Factor all algebraic quantities in the numerators and the denominators. Cancel common factors appearing in both a numerator and a denominator.

Multiplying Rational Expressions Express the result as the product of the numerators divided by the product of the denominators.

Example 3 x2 + 2xy + y2 18 • = 2x + 2y x2 – y2 (x + y)(x + y) 18 • = • = 9 (x + y)(x + y) 2(x + y) 18 (x + y)(x – y) • = 1 9 x – y

Dividing Rational Expressions To divide by a fraction, multiply by the reciprocal of the divisor. This same procedure is used for dividing rational expressions.

Example 5 x2 3y2 x 9y Divide by . x2 3y2 x 9y ÷ = x2 3y2 9y x • = xx ÷ = x2 3y2 9y x • = xx 3yy 9y x • = 3x y

Example 6 x2 + 3x + 2 x2 + 2x + 1 ÷ = x2 + x – 2 x2 – 1 x2 + 3x + 2 ÷ = x2 – 1 x2 + 2x + 1 • = x2 + 3x + 2 x2 + x – 2 (x + 2)(x + 1) (x + 2)(x – 1) (x – 1)(x + 1) (x + 1)(x + 1) • =

Example 6 (x + 2)(x + 1) (x – 1)(x + 1) 1 • = (x + 2)(x – 1) • = 1

Example 7 These techniques can be used to convert unit rates. Treat each unit as a factor and arrange the unit multipliers to cancel the original units.

Example 7 60 mi hr 5280 ft 1 mi • 1 hr 60 min • 1 min 60 sec • = = 88 ft/sec

Homework: pp. 540-541