Q: Which of the following is equivalent to dividing $$\frac{4}{9} by$$ $$-\frac{2}{3}$$?

$$-\frac{2}{3}$$ \rightarrow \frac{4}{9} \div -\frac{2}{3} = \frac{4}{9} \times -\frac{3}{2} = -\frac{12}{18} = -\frac{2}{3}$

Question 1

Which of the following is the correct reciprocal of $$-\frac{5}{7}$$?

Accepted Answer

$$-\frac{7}{5}$$

Question 2

A chemist mixes two solutions. The first contains $$\frac{3}{8}$$ liters of acid, and the second contains $$-\frac{1}{8}$$ liters (a base neutralizing acid). What is the total amount of acid after mixing?

Accepted Answer

$$\frac{2}{8}$$ liters

Question 3

Evaluate the expression $$2x - 3y$$ when $$x = -4$$ and $$y = 5.$$

Accepted Answer

$$-23$$

Question 4

Which of the following is the least common multiple (LCM) of 6 and 8?

Accepted Answer

$$24$$

Question 5

A medical researcher records a temperature change of $$-\frac{2}{3}$$ degrees, then another change of $$-\frac{1}{3}$$ degrees. What is the total change?

Accepted Answer

$$-1$$ degree

Question 6

Which of the following correctly applies the order of operations to $$3 + 2 	imes (4 - 1)^2$?

Accepted Answer

$$21$$

Question 7

A student subtracts $$-\frac{5}{6}$$ from $$\frac{1}{6}. $$What is the result?

Accepted Answer

$$1$$

Question 8

Which of the following is equivalent to dividing $$\frac{4}{9} by$$ $$-\frac{2}{3}$$?

Accepted Answer

$$-\frac{2}{3}$$ ightarrow \frac{4}{9} \div -\frac{2}{3} = \frac{4}{9} 	imes -\frac{3}{2} = -\frac{12}{18} = -\frac{2}{3}$

Question 9

If $$a = -2$$ and $$b = 3$$, what is the value of $$-(a^2) + 2b$?

Accepted Answer

$$6$$

Question 10

A recipe calls for $$\frac{1}{4}$$ cup of oil, but you accidentally add $$-\frac{1}{2}$$ cup. What is the net amount of oil in the mixture?

Accepted Answer

$$-\frac{1}{4}$$ cup

Question 11

Which of the following is the correct result of multiplying $$-\frac{3}{5} by$$ $$\frac{2}{7}$$?

Accepted Answer

$$-\frac{6}{35}$$

Question 12

Evaluate $$2(x - y)^2$ when x = 1$ and y = -2$.

Accepted Answer

$$18$$

Question 13

Which of the following is the correct result of $$-\frac{4}{9} + \frac{2}{9}$$?

Accepted Answer

$$-\frac{2}{9}$$

Question 14

A business lost $$-\frac{3}{10}$$ million dollars last year and gained $$\frac{1}{5}$$ million dollars this year. What is the net change?

Accepted Answer

$$-\frac{1}{10}$$ million dollars

Question 15

Which of the following is the correct result of $$\frac{5}{12} 	imes -\frac{3}{4}$$?

Accepted Answer

$$-\frac{15}{48}$$

Question 16

If $$x = -3$$ and $$y = 2$$, what is the value of $$x^2 - 4y$?

Accepted Answer

$$1$$

Question 17

Which of the following is the correct result of $$\frac{7}{8} \div -\frac{1}{4}$$?

Accepted Answer

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

Question 18

A scientist needs to add $$\frac{1}{3}$$ grams of a compound to a solution, but accidentally adds $$-\frac{1}{6}$$ grams. What is the net amount added?

Accepted Answer

$$\frac{1}{6}$$ grams

Question 19

Which of the following is the correct result of $$-\frac{2}{5} - (-\frac{3}{10})$$?

Accepted Answer

$$-\frac{1}{10}$$

Question 20

Evaluate $$3x^2 - 2y$ when x = -1$ and y = -4$.

Accepted Answer

$$10$$

Operations on Numbers: Foundations for College Algebra

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