Here's the solution to each problem with a clear explanation:
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Problem 1:
> During summer, the height of the water in a pool decreases by 4 inches each week due to evaporation. What is the change in the height of the water over a six-week period?
Solution:
Each week, the water level
decreases by 4 inches → this is a
negative change:
–4 inches/week
Over 6 weeks:
→ Change = 6 weeks × (–4 inches/week) =
–24 inches
✔ Answer: D) –24 Inches
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Problem 2:
> On a rainy day, the amount of rain in a rain gauge increased by 8 inches over a 24-hour period. How much did the amount of rain in the gauge increase by over an 8-day period?
Solution:
First, find the daily increase:
→ 8 inches per day
Over 8 days:
→ Increase = 8 days × 8 inches/day =
64 inches
✔ Answer: A) 64 Inches
*(Note: The question says “increase,” so we expect a positive number.)*
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Problem 3:
> After vigorous activity, your heart rate declines 12 beats per minute. How many beats per minute does your heart rate decline in one-half minute?
Solution:
Heart rate declines at a rate of
–12 beats per minute
In
half a minute (0.5 minutes):
→ Decline = 0.5 × (–12) =
–6 beats
✔ Answer: A) –6 Beats
*(This makes sense — if it drops 12 beats in a full minute, it drops half that amount in half a minute.)*
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Problem 4:
> On a certain day, the temperature changed at a rate of –3°F per hour. How long did it take for the change in temperature to be –30°F?
Solution:
Rate of change =
–3°F per hour
Total change needed =
–30°F
Time = Total Change ÷ Rate
→ Time = (–30°F) ÷ (–3°F/hour) =
10 hours
✔ Answer: C) 10 Hours
*(Negative divided by negative gives positive time — which makes sense.)*
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Problem 5:
> During a 12-hour period, the temperature dropped 48°. How many degrees did the temperature drop each hour?
Solution:
Total drop =
–48°F (since it dropped)
Time = 12 hours
Rate per hour = Total Change ÷ Time
→ Rate = (–48°F) ÷ 12 hours =
–4°F per hour
✔ Answer: D) –4°F
*(The question asks “how many degrees did the temperature drop each hour?” — since it’s a drop, the answer should be negative.)*
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✔ Final Answers:
1.
D) –24 Inches
2.
A) 64 Inches
3.
A) –6 Beats
4.
C) 10 Hours
5.
D) –4°F
Let me know if you’d like a visual diagram or further breakdown!
Parent Tip: Review the logic above to help your child master the concept of dividing integers word problems worksheet.
