Adding and Subtracting Integers

Show your work for each problem.

1.
What is $(-3) + (-5)$ ?
1. a) $-2$
2. b) $-8$
3. c) $8$
4. d) $2$
Answer: $-8$
When adding two negative numbers, add the absolute values ( $3 + 5 = 8$ ) and keep the negative sign: $(-3) + (-5) = -8$ .
2.
What is $7 + (-4)$ ?
1. a) $-3$
2. b) $-11$
3. c) $3$
4. d) $11$
Answer: $3$
Different signs: $|7| - |{-4}| = 7 - 4 = 3$ . Since $7 > 4$ and $7$ is positive, the answer is $3$ .
3.
Calculate: $(-6) + (-2)$
Answer: -8
Same signs (both negative): Add $6 + 2 = 8$ , then apply the negative sign: $-8$ .
4.
Calculate: $(-8) + 5$
Answer: -3
Different signs: $|{-8}| - |5| = 8 - 5 = 3$ . Since $8 > 5$ and $-8$ is negative, the answer is $-3$ .
5.
Calculate $(-4) + 9$ using the rules for adding integers.
Answer: 5
1. Are the signs the same or different? different
2. What is $|{-4}|$ ? 4
3. What is $|9|$ ? 9
4. Subtract: $9 - 4 = ?$ 5
5. Since $9 > 4$ and $9$ is positive, the final answer is? 5
6.
What is $5 - 12$ ?
1. a) $17$
2. b) $-7$
3. c) $-17$
4. d) $7$
Answer: $-7$
$5 - 12 = 5 + (-12)$ . Different signs: $12 - 5 = 7$ . Since $12 > 5$ and $-12$ is negative, the answer is $-7$ .
7.
What is $(-3) - (-10)$ ?
1. a) $13$
2. b) $-13$
3. c) $-7$
4. d) $7$
Answer: $7$
$(-3) - (-10) = (-3) + 10$ . Different signs: $10 - 3 = 7$ . Since $10 > 3$ and $10$ is positive, the answer is $7$ .
8.
Calculate: $(-7) - 4$
Answer: -11
$(-7) - 4 = (-7) + (-4)$ . Same signs: $7 + 4 = 11$ , keep the negative sign: $-11$ .
9.
Calculate: $6 - (-8)$
Answer: 14
$6 - (-8) = 6 + 8 = 14$ . The double negative becomes a positive!
10.
Calculate $(-5) - (-12)$ step by step.
Answer: 7
1. Rewrite $(-5) - (-12)$ as addition. What does it become? (-5) + 12
2. Are the signs the same or different? different
3. Subtract the absolute values: $12 - 5 = ?$ 7
4. Since $12 > 5$ and $12$ is positive, the final answer is? 7
11.
The temperature was $-8°C$ in the morning. By afternoon it rose 15 degrees. What is the afternoon temperature?
Answer: 7
1. What expression represents this situation? -8 + 15
2. Are the signs the same or different? different
3. Subtract: $15 - 8 = ?$ 7
4. What is the afternoon temperature in °C? 7
12.
What is $(-15) + 8 + (-3)$ ?
1. a) $10$
2. b) $-20$
3. c) $-26$
4. d) $-10$
Answer: $-10$
$(-15) + 8 = -7$ . Then $(-7) + (-3) = -10$ .
13.
Calculate: $(-12) - (-7) + (-5)$
Answer: -10
$(-12) - (-7) = (-12) + 7 = -5$ . Then $(-5) + (-5) = -10$ .
14.
Calculate: $25 - 40 + 8$
Answer: -7
$25 - 40 = -15$ . Then $(-15) + 8 = -7$ .
15.
A submarine is at $-45$ meters. It rises 30 meters, then dives 20 meters. What is its final depth?
Answer: -35
1. What expression represents this? (start + rise + dive) -45 + 30 + (-20)
2. Calculate $(-45) + 30$ -15
3. Now add $(-20)$ to $-15$ -35
4. What is the final depth in meters? -35
16.
Your bank account has 50 euros. You withdraw 75 euros, then deposit 30 euros. What is your balance?
Answer: 5
1. Write the expression (balance - withdrawal + deposit) 50 - 75 + 30
2. Rewrite $50 - 75$ as addition 50 + (-75)
3. Calculate $50 + (-75)$ -25
4. Now add $30$ to $-25$ 5
5. What is your final balance in euros? 5