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 = 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 -4xy 10x

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

Example x9 x2 x3 x5 x7 x3

Example 35x3yz6 56x5yz

Example (2ab)2 2ab2

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

Find the GCF of 72x3yz3 and 120x2z5 Example Find the GCF of 72x3yz3 and 120x2z5

Questions

Assignment Worksheet