Adding Integers
Find the sum: -8 + (-6).
Answer: -14
Explanation: Since both numbers are negative, you just add them together like normal numbers and keep the negative sign.
12 - 19
Answer: -7
Explanation: You are subtracting a bigger number from a smaller number, which pushes you past zero into the negative numbers.
Find the product: (-9)(4)
Answer: -36
Explanation: Whenever you multiply a negative number by a positive number, the answer is always negative.
Find the quotient: -63 ÷ 7
Answer: -9
Explanation: A negative number divided by a positive number always results in a negative answer.
-6 + 4(-3)
Answer: -18
Explanation: Order of operations says you have to multiply before adding. So you do 4 × (-3) = -12 first, and then do -6 + (-12) to get -18.
Find the sum: 17 + (-9)
Answer: 8
Explanation: The signs are different, so you subtract 9 from 17. Since 17 is the bigger number and it's positive, the answer stays positive.
-7 - (-13)
Answer: 6
Explanation: Using keep-change-flip, the double negative turns into addition, making it -7 + 13. Since the signs are different, you do 13 - 7 to get 6.
Find the product: (-8)(-7)
Answer: 56
Explanation: When you multiply two negative numbers together, the signs cancel out and give you a positive answer.
Find the quotient: -96 ÷ (-12)
Answer: 8
Explanation: Dividing a negative number by another negative number always gives you a positive answer.
Solve: 36 ÷ (-6) + 8
Answer: 2
Explanation: You have to divide first, so 36 ÷ (-6) = -6. Then you add 8, which leaves you with a positive 2.
-24 + 15
Answer: -9
Explanation: Subtract 15 from 24 to get 9. Since -24 is farther from zero than 15, the answer takes the negative sign.
-18 - 9
Answer: -27
Explanation: Subtracting 9 from a negative number means you are moving further left on the number line, which is the same as doing -18 + (-9).
Find the product: (-3)(5)(-2)
Answer: 30
Explanation: First, do -3 times 5, which equals -15. Then, multiply -15 by -2. Since a negative times a negative is positive, it equals 30.
Find the quotient: 144 ÷ (-16)
Answer: -9
Explanation: A positive number divided by a negative number results in a negative answer.
Solve: 18 - (-4)(3)
Answer: 30
Explanation: Multiply first: (-4) × 3 = -12. Now the problem looks like 18 - (-12). The double negative turns into addition, so 18 + 12 = 30.
A submarine is 35 feet below sea level and rises 18 feet. What is its new position?
Answer: -17 feet (or 17 feet below sea level)
Explanation: Below sea level means starting at -35. Rising means adding 18. Since the signs are different, you find the difference between 35 and 18, which leaves you at -17.
The temperature is 4°F and drops 11°F. What is the new temperature?
Answer: -7°F
Explanation: You start at 4 and subtract 11 because the temperature dropped. Since 11 is bigger than 4, it drops below zero down to -7.
A hiker loses 6 feet of elevation during each of 4 sections. What is the total change in elevation?
Answer: -24 feet (or a loss of 24 feet)
Explanation: Losing elevation is negative, so it is written as -6. Since it happens 4 times, you multiply -6 by 4 to get -24.
A bank account loses $240 over 8 equal withdrawals. What is the change from each withdrawal?
Answer: -$30 (or a decrease of $30)
Explanation: A total loss is written as -240. Since it's split up into 8 equal parts, you divide -240 by 8, which gives you -30 for each one.
Solve: -5[7 + (-11)] - 6
Answer: 14
Explanation: Solve inside the brackets first: 7 + (-11) = -4. Next, multiply -5 by -4, which gives you a positive 20. Finally, subtract 6 to get 14.
Explain the rule for adding integers with different signs
Explanation: When you add numbers with different signs, you actually subtract the smaller number from the bigger number. Then, you look at which number was bigger to begin with and use its sign for your final answer.
Explain why 15 - (-6) has a positive answer.
Explanation: It has a positive answer because subtracting a negative number is the exact same thing as adding a positive number. The two minus signs cancel out and turn into a plus, making the problem 15 + 6 = 21.
Find the product and explain its sign: (-2)(-5)(-4)(3)
Answer: -120
Explanation: If you multiply across, (-2) × (-5) is 10. Then 10 × (-4) is -40. Finally, -40 × 3 is -120. The final answer is negative because there is an odd number of negative signs in the problem.
Use multiplication to check whether -84 ÷ (-7) = 12 is correct.
Explanation: To check it, you just multiply the answer by the number you divided by: 12 × (-7). Since a positive times a negative is negative, 12 × -7 equals -84, proving the division was right.
A video game score changes by -3 points during each of 6 rounds, then increases by 45 points, and loses 18 points divided equally among 3 players. What is the final change in one player's score?
Answer: 6 points
Explanation: First, find the score after the rounds: -3 × 5 = -15. Then add the 43 points: -15 + 43 = 28. Next, subtract the 16 lost points: 28 - 16 = 12. Finally, split that total score change equally between the 2 players: 12 ÷ 2 = 6.