How Do You Divide Quotients of Monomials?

How Do You Divide Quotients of Monomials?

Note:

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.

Keywords:

  • problem
  • rational
  • rational expression
  • divide
  • reciprocal
  • multiply
  • reduce
  • factor
  • fraction
  • algebraic fraction
  • variable
  • monomial
  • quotient
  • quotient of powers
  • division
  • cancel
  • divide fractions
  • divide rational expressions

Background Tutorials

  • Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

      • What's the Reciprocal Rule of Division?What's the Reciprocal Rule of Division?

      What's the Reciprocal Rule of Division?

      When you divide fractions, the trick is to rewrite division as a multiplication. But the truth is that you can always rewrite division as a multiplication, and in this tutorial you'll see the rule that makes that possible!

  • 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.

  • 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 Reduce Common Factors in a Rational Expression?How Do You Reduce Common Factors in a Rational Expression?

      How Do You Reduce Common Factors in a Rational Expression?

      Multiplying rational expressions? Want to cancel common factors out to make things easier to work with? In this tutorial, you'll see how to cancel out common factors in order to find the simplified product of two rational expression. Check it out!

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.