Q: Which of the following correctly applies the order of operations to $$8 - 2 \times (3 + 1)^2$?

$$8 - 2 \times 16 = 8 - 32 = -24$$

Question 1

Which of the following expressions is equivalent to $$-18 - (-9) + (-4)$$?

Accepted Answer

$$-18 + 9 - 4$$

Question 2

Evaluate the following expression using the order of operations: $$3 \cdot (-4)^2$ - 20 \div (-5)$$

Accepted Answer

$$52$$

Question 3

What is the absolute value of $$-14$$ plus the absolute value of $$6$$ minus the absolute value of $$-5$$?

Accepted Answer

$$15$$

Question 4

A submarine is at $$-120$$ meters below sea level. It ascends $$45$$ meters, then descends $$30$$ meters. What is its final position relative to sea level?

Accepted Answer

$$-105$$ meters

Question 5

Which of the following is a rational number?

Accepted Answer

$$-\frac{28}{42}$$

Question 6

Simplify $$-\frac{28}{42} to $$lowest terms.

Accepted Answer

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

Question 7

Multiply: $$-\frac{4}{5} \cdot \frac{15}{16}$$

Accepted Answer

$$-\frac{3}{4}$$

Question 8

Divide: $$\frac{7}{12} \div -\frac{14}{3}$$

Accepted Answer

$$-\frac{1}{8}$$

Question 9

A recipe calls for $$\frac{3}{8}$$ cup of oil and $$\frac{5}{12}$$ cup of vinegar. How much more oil than vinegar does the recipe use?

Accepted Answer

$$\frac{1}{24}$$ cup

Question 10

Which of the following correctly applies the order of operations to $$8 - 2 	imes (3 + 1)^2$?

Accepted Answer

$$8 - 2 	imes 16 = 8 - 32 = -24$$

Question 11

A medical thermometer reads $$-3$$ degrees Celsius. If the temperature increases by $$7$$ degrees and then drops by $$5$$ degrees, what is the final temperature?

Accepted Answer

$$-1$$ degrees Celsius

Question 12

Add: $$-\frac{3}{8} + \frac{5}{12}$$

Accepted Answer

$$\frac{1}{24}$$

Question 13

Which of the following is the correct way to subtract $$a - b$$ according to the subtraction rule?

Accepted Answer

$$a + (-b)$$

Question 14

A hiker descends $$250$$ meters, then ascends $$120$$ meters, and finally descends another $$80$$ meters. What is the hiker's net change in elevation?

Accepted Answer

$$-210$$ meters

Question 15

Which of the following is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 16

If $$a = -6$$ and $$b = 2$$, what is $$|a| + |b| - |-a|$$?

Accepted Answer

$$2$$

Question 17

A chemist mixes $$\frac{2}{3}$$ liter of solution A with $$\frac{1}{4}$$ liter of solution B. What is the total volume of the mixture?

Accepted Answer

$$\frac{11}{12}$$ liters

Question 18

Which of the following is the correct result of dividing $$\frac{5}{8} by$$ $$\frac{10}{3}$$?

Accepted Answer

$$\frac{3}{16}$$

Question 19

A student spends $$\frac{3}{5} of an $$hour on math homework and $$\frac{1}{4} of an $$hour on science homework. How much more time did the student spend on math than science?

Accepted Answer

$$\frac{7}{20}$$ hours

Question 20

Which of the following is the correct simplification of $$\frac{18}{24}$$?

Accepted Answer

$$\frac{3}{4}$$

Prealgebra Study Guide: Integers, Order of Operations, and Rational Numbers

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