Dividing Complex Fractions

Dividing Complex Fractions

​

Multiple Choice

Finish this sentence:

Dividing by a number is the same as........

• multiplying by the reciprocal

• multiplying

• the reciprocal

• dividing by the reciprocal

Multiple Choice

What should be your first step, if you have this problem?

$$\frac{x}{2y}\div\frac{xy}{4}$$  

• $$\frac{x}{2y}\cdot\frac{4}{xy}$$  

• $$\frac{x}{2y}\cdot\frac{xy}{4}$$  

• $$\frac{2y}{x}\cdot\frac{4}{xy}$$  

• $$\frac{2y}{x}\cdot\frac{xy}{4}$$  

Multiple Choice

What is the first step?

$$\frac{x^2-y^2}{x^2+y^2}\div\left(x+y\right)$$  

• $$\frac{x^2-y^2}{x^2+y^2}\cdot\frac{1}{\left(x+y\right)}$$  

• $$\frac{x^2-y^2}{x^2+y^2}\cdot\frac{\left(x+y\right)}{1}$$  

Multiple Choice

If you have this problem, what should be your first step?  

$$\frac{18}{x^2-25}\div\frac{24}{x+5}$$  

• $$\frac{18}{x^2-25}\cdot\frac{x+5}{24}$$  

• $$\frac{x^2-25}{18}\cdot\frac{24}{x+5}$$  

Multiple Choice

So now you are back to the exact same problems you did for homework. So what should be your next step, if this is your problem?

$$\frac{18}{x^2-25}\cdot\frac{x+5}{24}$$  

• Factor

• Cross off like terms

• Multiply the numerators

• Multiply the denominators

Multiple Choice

What is your first step here?

$$\frac{x^2+3x-10}{2x+6}\div\frac{x^2-4}{x^2-x-12}$$  

• $$\frac{x^2+3x-10}{2x+6}\cdot\frac{x^2-4}{x^2-x-12}$$  

• $$\frac{x^2+3x-10}{2x+6}\cdot\frac{x^2-x-12}{x^2-4}$$  

Multiple Choice

So you now GCF and Factor, which is the correct next step?

$$\frac{x^2+3x-10}{2x+6}\cdot\frac{x^2-x-12}{x^2-4}$$  

• $$\frac{\left(x+5\right)\left(x-2\right)}{2\left(x+3\right)}\cdot\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}$$  

• $$\frac{\left(x+5\right)\left(x-2\right)}{2x+6}\cdot\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}$$  

• $$\frac{\left(x+5\right)\left(x-2\right)}{2\left(x+3\right)}\cdot\frac{\left(x-2\right)\left(x+2\right)}{\left(x-4\right)\left(x+3\right)}$$  

Multiple Choice

So now finish the problem

$$\frac{\left(x+5\right)\left(x-2\right)}{2\left(x+3\right)}\cdot\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}$$  

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

• $$\frac{x^2-20}{2x-4}$$  

• $$\frac{\left(x+5\right)}{\left(x+2\right)}$$  

Multiple Choice

This problem has been factored for you. What is the final answer?

$$\frac{\left(2x+1\right)\left(x-2\right)}{\left(x+3\right)}\cdot\frac{\left(x-3\right)}{\left(1+2x\right)\left(2-x\right)}$$  

• $$-\frac{x-3}{x+3}$$  

• $$\frac{x-3}{x+3}$$  

• $$-1$$  

• $$1$$