Working with Integers Practice Questions

Introduction

For some people, it is helpful to try to simplify expressions containing signed numbers as much as possible. When you find signed numbers with addition and subtraction operations, you can simplify the task by changing all subtraction to addition. Subtracting a number is the same as adding its opposite. For example, subtracting a three is the same as adding a negative three. Or subtracting a negative 14 is the same as adding a positive 14. As you go through the step-by-step answer explanations, you will begin to see how this process of using only addition can help simplify your understanding of operations with signed numbers. As you begin to gain confidence, you may be able to eliminate some of the steps by doing them in your head and not having to write them down. After all, that's the point of practice! You work at the problems until the process becomes automatic. Then you own that process and you are ready to use it in other situations.

The Tips for Working with Integers section that follows gives you some simple rules to follow as you solve problems with integers. Refer to them each time you do a problem until you don't need to look at them. That's when you can consider them yours.

You will also want to review the rules for Order of Operations with numerical expressions. You can use a memory device called a mnemonic to help you remember a set of instructions. Try remembering the word

PEMDAS. This nonsense word helps you remember to:

P           do operations inside Parentheses

E           evaluate terms with Exponents

M D     do Multiplication and Division in order from left to right

A S      Add and Subtract terms in order from left to right

Tips for Working with Integers

Addition

Signed numbers the same? Find the SUM and use the same sign. Signed numbers different? Find the DIFFERENCE and use the sign of the larger number. (The larger number is the one whose value without a positive or negative sign is greatest.)

Addition is commutative. That is, you can add numbers in any order and the result is the same. As an example, 3 + 5 = 5 + 3, or ^–2 + ^–1 = ^–1 + –2.

Subtraction

Change the operation sign to addition, change the sign of the number following the operation, then follow the rules for addition.

Multiplication/Division

Signs the same? Multiply or divide and give the result a positive sign. Signs different? Multiply or divide and give the result a negative sign.

Multiplication is commutative. You can multiply terms in any order and the result will be the same. For example: (2 · 5 · 7) = (2 · 7 · 5) = (5 · 2 · 7) = (5 · 7 · 2) and so on.

Practice Questions

Evaluate the following expressions.

1. 27 + ^–5
2. ^–18 + ^–20 – 16
3. ^–15 – ^–7
4. 33 + ^–16
5. 8 + ^–4 – 12
6. 38 ÷ ^–2 + 9
7. ^–25 · ^–3 + 15 · ^–5
8. ^–5 · ^–9 · ^–2
9. 24 · ^–8 + 2
10. 2 · ^–3 · ^–7
11. ^–15 + 5 + ^–11
12. (49 ÷ 7) – (48 ÷ ^–4)
13. 3 + ^–7 – 14 + 5
14. ^–(5 · 3) + (12 ÷ ^–4)
15. (^–18 ÷ 2) – (6 · ^–3)
16. 2³ + (64 ÷ ^–16)
17. 2³ – (^–4)²
18. (3 – 5)³ + (18 ÷ 6)²
19. 21 + (11 + ^–8)³
20. (3² + 6) ÷ (^–24 ÷ 8)
21. A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then rises 52 feet where he will do a safety stop for five minutes before surfacing. At what depth did he do his safety stop?
22. A digital thermometer records the daily high and low temperatures. The high for the day was ⁺5° C. The low was ^–12° C. What was the difference between the day's high and low temperatures?
23. A checkbook balance sheet shows an initial balance for the month of $300. During the month, checks were written in the amounts of $25, $82, $213, and $97. Deposits were made into the account in the amounts of $84 and $116. What was the balance at the end of the month?
24. A gambler begins playing a slot machine with $10 in quarters in her coin bucket. She plays 15 quarters before winning a jackpot of 50 quarters. She then plays 20 more quarters in the same machine before walking away. How many quarters does she now have in her coin bucket?
25. A glider is towed to an altitude of 2,000 feet above the ground before being released by the tow plane. The glider loses 450 feet of altitude before finding an updraft that lifts it 1,750 feet. What is the glider's altitude now?