Dividing Monomials Chapter 5 Section 5 2 Objective

Dividing Monomials Chapter 5 Section 5. 2

Objective Students will simplify quotients of monomials and find the greatest common factor (GCF) of several monomials

Concept There are three basic rules used to simplify fractions whose numerators and denominators are monomials. The property of quotients allows you to express a fraction as a product.

Concept Property of Quotients If a, b, c, and d are real numbers with b ≠ 0 and d ≠ 0, then ac = a * c bd b d

Example 15 = 3 * 5 = 1 * 5 = 5 21 3*7 3 7 7 7

Concept You obtain the following rule for simplifying fractions if you let a=b in the property of quotients.

Concept If b, c, and d are real numbers with b ≠ 0 and d ≠ 0, then bc = c bd d

Concept This rule allows you to divide the numerator and denominator of a fraction by the same nonzero number. In the examples of this lesson, assume that no denominator equals zero.

Concept A quotient of monomials is said to be simplified when each base appears only once, when there are no powers of powers, and when the numerator and denominator have no common factors other than 1.

Example 35 42 -4 xy 10 x

Concept Rule of Exponents for Division If a is a nonzero real number and m and n are positive integers then: If m > n am = am-n an If n > m am = 1 an an-m If m = n am = 1 an always subtract the smaller exponent from the larger

Example x 9 x 2 x 5 x 7 x 3

Example 35 x 3 yz 6 56 x 5 yz

Example (2 ab)2 2 ab 2

Concept The greatest common factor (GCF) of two or more monomials is the common factor with the greatest coefficient and the greatest degree in each variable. 1. Find the GCF of the numerical coefficients (prime factorization) 2. Find the smaller power of each variable in common 3. Write the product of the GCF and smaller power of variables

Example Find the GCF of 72 x 3 yz 3 and 120 x 2 z 5

Questions

Assignment Worksheet