How Do You Multiply Quotients of Monomials by Canceling Factors?

How Do You Multiply Quotients of Monomials by Canceling Factors?

Note:

Multiplying fractions made up of monomials is easier than you might think! You can cancel common factors in the numerator and denominator to make things easier to work with. Then just multiply to get your final answer! This tutorial will show you how.

Keywords:

  • problem
  • rational
  • rational expression
  • multiply
  • simplify
  • cancel
  • reduce
  • factor
  • fraction
  • algebraic fraction
  • monomial
  • variable
  • common factor
  • quotient of powers
  • variables
  • divide
  • multiply fractions
  • multiplication
  • multiply rational expressions

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Interpret parts of an expression, such as terms, factors, and coefficients.

      • What's a Factor?What's a Factor?

      What's a Factor?

      Factors are a fundamental part of algebra, so it would be a great idea to know all about them. This tutorial can help! Take a look!

  • Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

      • What's a Monomial?What's a Monomial?

      What's a Monomial?

      If you learn about algebra, then you'll see monomials everywhere! Watch this tutorial and learn what makes a monomial, and what does not.

Further Exploration

  • Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + (r(x)/b(x)), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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

      • How Do You Divide Quotients of Monomials?How Do You Divide Quotients of Monomials?

      How Do You Divide Quotients of Monomials?

      Dividing fractions made up of monomials is easier than you might think! First, turn it into a multiplication problem by multiplying by the reciprocal of the divisor. Then, you can cancel common factors in the numerator and denominator to make things easier to work with. Finally, multiply to get your final answer! This tutorial will show you how.

      • How Do You Multiply Quotients of Monomials?How Do You Multiply Quotients of Monomials?

      How Do You Multiply Quotients of Monomials?

      Multiplying together two monomials isn't so hard, especially if you know the proper steps! This tutorial will take you through all the steps necessary to multiply together two monomials. Then, you'll see how to divide the numerator and denominator by the greatest common factor (GCF) in order to simplify and get your answer!