Adding Integers
Find −21 + (−9) + 18. Identify what rules you used
adding two integers with the same sign and adding two integers with different signs.
Answer: -12
Find –42 – (–61). Identify which rule you used.
adding two integers with different signs
Answer: 19
Amelia bought 7 ride tickets with her debit card. Each ticket costs $3.
What integer represents the change in her balance, in dollars, after buying the tickets? (Write the equation, the rules, and the answer)
7 x (-3) or (-3) x 7
The rule: the answer will be negative
The answer: -21
Tony made 4 withdrawals last month. Each time, he withdrew the same amount. If Tony withdrew a total of $504, what integer represent the change in his account after each withdrawal? (write the equation, the rule, and the answer)
504 / (-4)
the rule: when dividing two integers with different signs the answer is always negative
the answer: -126
Find 9×(−5)×(−2)−(−16).
106
Find 16 + (−11) + 8. Identify which rules you used.
adding two integers with different signs and adding to integers with the same sign.
Answer: 13
Find 15 − (−58). Identify what rule you used.
adding two integers with the same sign
Answer: 73
Every day, 2 inches of water evaporated from the pond.
What integer represents the change in the depth of the pond, in inches, after 17 days? (Write down the equation, the rules, and the answer)
(-2) x 17 or 17 x (-2)
The rule: when multiplying two integers with different signs the answer is always negative
The answer: -34
Iman walks down 24 steps, and her vertical height decreases by 240 inches. What integer represents the average change in Iman’s vertical height, in inches, as she walks down each step? (write the equation, the rule, and the answer)
240 / (-24)
the rule: when dividing two integers with different signs the answer will always be negative
the answer: -10
Find 3×(−6)×(−7)−(−18).
144
A whale swam at a depth of 275 feet below the surface of the ocean. After 10 minutes, it rose 194 feet.
What integer represents the location of the whale, relative to the ocean’s surface in feet, after 10 minutes? (write the equation, the rule, and the answer)
(-275) + 194 or 194 + (-275)
the rule: when adding two integers with different signs you subtract like normal and then keep the sign of the integer with the highest absolute value
the answer: -81
The highest point in a park is 235 feet above sea level. The lowest point is 32 feet below sea level. What is the distance between the highest and lowest points in the park?
267
The temperature of a cup of coffee dropped 18°F every minute for 6 minutes.
What integer represents the total change in the temperature of the coffee, in degrees Fahrenheit, after 6 minutes? (Write the equation, the rule, and the answer).
(-18) x 6 or 6 x (-18)
The rule: when multiplying two integers with different signs, the answer will always be negative.
The answer: -108
A ball floats 560 feet to the top of a swimming pool in 4 seconds. At this rate, what integer represents the change, in feet, of the ball’s position after one second? (write the equation, the rule, and the answer)
560 / 4
the rule: when dividing two integers with the same sign, the answer is always positive.
the answer: 140
Evaluate the expression. 512 / 4×4 - [(-64) + (-96)]
192
In 30 seconds, a mountain biker goes up a 125-foot hill, then down 78 feet, and then back up a 32-foot hill. What integer represents the vertical change from the start of the trail to where the biker is after 30 seconds?
79
The highest point in South America is Mount Aconcagua at 22,838 feet. The lowest point in South America is Laguna del Carbon at 344 feet below sea level. What is the distance between the highest and lowest points in South America?
23,182
A scuba diver ascends above the surface of a lake at a rate of 205 feet per minute. What integer represents the depth of the diver after 8 minutes? (Write the equation, the rules, and the answer)
205 x 8
The rule: when multiplying two integers with the same sign the answer is always positive.
The answer: 1,640
The number of students attending Meadowlawn Middle School increased by 288 over a 4-year period. What integer represents the average yearly change in enrollment? (write the equation, the rule, and the answer)
288 / 4
the rule: when dividing two integers with the same sign, the answer will always be positive
the answer: 72
Use the expression 5 × (59-32) / 9 to convert 59 degrees Fahrenheit to degrees Celsius.
15
In 8 minutes, an elevator goes up 17 floors, then down 23 floors, and then back up 4 floors. What integer represents the vertical change from where the elevator started to where the elevator is after 8 minutes?
The highest and lowest temperatures on Mercury are 870° Fahrenheit and −300° Fahrenheit. Find the range of these extreme temperatures.
1,170
During a period of time a reservoir is drained for 2 hours per day 3 times per week. Each time 12 gallons per minute are drained. What integer represents the change in the number of gallons drained from the reservoir each week? (Write down the equation, the rules, and the answer)
(-120) x 3 and (-360) x 12
The rule: when multiplying two integers with different signs the answer is always negative
The answer: -4,320
During a 5-day workweek, the price of a stock decreased by 345 points. What integer represents the average daily change in the stock price for the workweek? (write the equation, the rule, and the answer)
(-345) / 5
The rule: when dividing two integers with different signs the answer is always negative
The answer: -69
The table gives the income and expenses of a rental company for one year. Use the expression 64,200–72,000 / 12 to find the average difference between the company’s income and expenses each month.
-650