Question 1

Which of the following correctly simplifies $$\frac{6x}{12x}$$?

Accepted Answer

$$\frac{1}{2}$$

Question 2

A medical dosage formula is $$\frac{a}{b}$$, where $$a is $$the amount of drug and $$b is $$the patient's weight. If a patient weighs twice as much, what happens to the dosage per pound?

Accepted Answer

It halves

Question 3

Which of the following is a valid simplification of $$\frac{x(x+2)}{x(x-3)}$$?

Accepted Answer

$$\frac{x+2}{x-3}$$

Question 4

A chemical reaction produces $$\frac{2}{3}$$ liters of solution per batch. If you run 5 batches, how much solution do you have?

Accepted Answer

$\frac{10}{3}$$ liters

Question 5

What is the result of $$\left(\frac{3}{4}\right) \div \left(\frac{2}{5}\right)$$?

Accepted Answer

$$\frac{15}{8}$$

Question 6

If $$\frac{x}{x+9} = \frac{6}{5}$$, what is the value of $$x$$?

Accepted Answer

Question 7

Which of the following is NOT a valid property for splitting fractions?

Accepted Answer

$$\frac{a}{b+c} = \frac{a}{b} + \frac{a}{c}$$

Question 8

A student tries to simplify $$\frac{x+2}{x+3} by $$canceling $$x$$ terms. What is the correct response?

Accepted Answer

You can only cancel common factors, not terms

Question 9

If $$\frac{x+3}{3} + \frac{x+5}{2} = 5$$, what is the first step to solve for $$x$$?

Accepted Answer

Find the LCD and multiply every term by it

Question 10

Which of the following is the correct restriction for $$\frac{x+1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 11

A hospital uses a formula $$\frac{a}{a} to $$check if a dosage is correct. What is the result, assuming $$a 
eq 0$$?

Accepted Answer

$$1$$

Question 12

Which of the following is undefined?

Accepted Answer

$$\frac{a}{0}$$

Question 13

What is the result of $$\frac{(x-3)}{(3-x)}$$?

Accepted Answer

$$-1$$

Question 14

Which of the following is equivalent to $$\frac{2}{3}$$?

Accepted Answer

$$\frac{8}{12}$$

Question 15

A recipe requires $$\frac{1}{4}$$ cup of oil per serving. If you make 8 servings, how much oil do you need?

Accepted Answer

$$2$$ cups

Question 16

Which property explains why $$\frac{-a}{b} = -\left(\frac{a}{b}\right)$$?

Accepted Answer

Negative signs in fractions

Question 17

If $$\frac{a}{b} + \frac{c}{b}$$, what is the result?

Accepted Answer

$$\frac{a+c}{b}$$

Question 18

A student subtracts $$\frac{x}{7} - \frac{2}{7}. $$What is the correct result?

Accepted Answer

$$\frac{x-2}{7}$$

Question 19

Which of the following is the correct way to clear denominators in $$\frac{5}{x+3} = 2$$?

Accepted Answer

Multiply both sides by $$x+3$$

Question 20

A student multiplies $$\frac{2}{3} 	imes \frac{5}{7}. $$What is the result?

Accepted Answer

$$\frac{10}{21}$$

Division and Quotient Properties in Algebra: A Study Guide

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