Skip to the content

Alpha

Flip-Top Fred

Flip-Top FredFractioneers · rational expressions and functions

Flips its top and bottom over to divide: multiplying and dividing rational expressions.

Multiplying and Dividing Rational Expressions

Multiplying and dividing rational expressions. In MathBound, the free Algebra I adventure game, Flip-Top Fred asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Multiply Rational Expressions. Multiply rational expressions consisting of monomials by multiplying straight across and using exponent properties.
Divide Rational Expressions. Divide rational expressions consisting of monomials by rewriting as multiplication by the reciprocal.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Multiply Rational Expressions

Multiply:

\frac{- 6 x ^{3}}{5 y ^{2}} \cdot \frac{5 y ^{3}}{4 x}

$\frac{3 x ^{2} y}{2}$
$\frac{- 3 x ^{4} y ^{5}}{2}$
$\frac{- 2}{3 x ^{2} y}$
$\frac{- 3 x ^{2} y}{2}$

Show the worked steps

$Multiply$ $across:$ $\frac{- 30 x ^{3} y ^{3}}{20 x y ^{2}} .$
$Reduce,$ $keeping$ $the$ $minus$ $sign:$ $\frac{- 3 x ^{2} y}{2} .$

Answer: $\frac{- 3 x ^{2} y}{2}$

Example 2 · Divide Rational Expressions

Divide:

\frac{\frac{24 a ^{3}}{5 b ^{3}}}{\frac{4 a}{15 b ^{6}}}

$6 a^{2} b^{3}$
$\frac{18 a ^{2}}{b ^{3}}$
$18 a^{4} b^{3}$
$18 a^{2} b^{3}$

Show the worked steps

$Dividing$ $is$ $multiplying$ $by$ $the$ $reciprocal:$ $flip$ $the$ $second$ $fraction.$
$Then$ $multiply$ $across$ $and$ $reduce.$

Answer: $18 a^{2} b^{3}$

Example 3 · Multiply Rational Expressions

Multiply:

\frac{3 x}{2} \cdot \frac{4}{3 x ^{2}} \cdot 4 x^{3}

$\frac{1}{8 x ^{2}}$
$\frac{2}{x}$
$8 x^{6}$
$8 x^{2}$

Show the worked steps

$Multiply$ $the$ $tops$ $and$ $the$ $bottoms:$ $\frac{48 x ^{4}}{6 x ^{2}} .$
$Reduce:$ $8 x^{2} .$

Answer: $8 x^{2}$

Where it is in your textbook

Textbook	Lessons
Glencoe Algebra 1	11-4
OpenStax Elementary Algebra 2e	8.2
Pearson Algebra 1 Common Core	11-2
SpringBoard Algebra 1	28

Ready for Flip-Top Fred?

Play this battle free Play the whole adventure