Multiplying and Dividing Rational Numbers

Multiplying and Dividing Rational Expressions

11/10

Open Ended

Do Now: Simplify the expression in the image.

Multiplying Rational Expressions

• Factor first (if possible)

• Cancel/Cross out common terms

• Multiply across

Multiplying Rational Expressions

• We can "cross cancel" because multiplication is commutative and because we are multiplying across

• Factor first, then reduce!! (same as simplifying)

Multiple Choice

Multiply the following expressions.

• $$\frac{8x^2y^7}{3x^3y^3}$$  

• $$\frac{8y^4}{3x}$$  

• $$\frac{40x^2y^7}{30x^3y^3}$$  

• $$\frac{12y^{10}}{50x^5}$$  

Multiple Choice

Multiply the following expressions.

• $$\frac{2x^4+4x^2-72x^2-144x}{4x^3+8x^2-144x-288}$$

• $$1$$

• $$\frac{x}{2}$$

• Can't be simplified

Dividing Rational Expressions

• Similar to multiplying rational expressions with one extra step in the beginning

• Can't divide by fractions so we have to flip it. (Keep Change Flip)

• Then we follow the steps to multiply rational expressions!

Multiple Choice

Divide the following expressions.

• $$\frac{y^{\ 4}}{2x^2}$$

• $$\frac{9y^8}{2x^4}$$

• $$\frac{2x^2}{y^{\ 4}}$$

• Can't be simplified

Multiple Choice

Divide the following expressions.

• $$\frac{4\left(x-4\right)}{\left(x+5\right)}$$

• $$\frac{\left(x+4\right)^2\left(x-4\right)}{16\left(x+5\right)}$$

• Can't be simplified

• $$\frac{\left(x+5\right)}{4\left(x-4\right)\ }$$

Dividing Rational Expressions

• Just like multiplying rational expressions with one extra step

• Always flip the rational expression that you are dividing by (second fraction or fraction in the denominator)

Please answer the next few questions

Multiple Choice

Multiply the following expressions.

$$\frac{x^2-8x+12}{x^2-16}\cdot\frac{4x+16}{x^2-4x+4}$$  

• $$\frac{4\left(x-6\right)}{\left(x-4\right)\left(x-2\right)}$$  

• $$\frac{\left(x-4\right)\left(x-2\right)}{4\left(x-6\right)}$$  

• $$\frac{x-6}{x-2}$$  

• $$\frac{4}{x-4}$$  

Open Ended

Explain in your own words how we simplify this expression.

Poll

How confident do you feel about your ability to multiply/divide rational expressions?

• Very Confident

• Pretty good, but need more practice

• Definitely need more practice

• Help me!