Let's solve each of the four problems step by step. All of them involve
division to find an
average rate of change over a period of time or events.
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1. STOCK MARKET
Problem:
During a 5-day workweek, the stock market decreased by 65 points. Find the average daily change in the market for the week.
Solution:
We are given:
- Total change = –65 points (negative because it decreased)
- Number of days = 5
To find the
average daily change, divide the total change by the number of days:
$$
\text{Average daily change} = \frac{-65}{5} = -13
$$
✔ Answer: The average daily change is
–13 points per day.
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2. MOTION
Problem:
Mr. Diaz decreased the speed of his car by 30 miles per hour over a period of 10 seconds. Find the average change in speed each second.
Solution:
We are given:
- Total change in speed = –30 mph (decreased)
- Time = 10 seconds
We want the
average change per second, so divide:
$$
\text{Average change per second} = \frac{-30}{10} = -3
$$
✔ Answer: The average change in speed is
–3 miles per hour per second.
> Note: This is a rate of deceleration — the car slows down by 3 mph each second.
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3. WEATHER
Problem:
Over the past seven days, Mrs. Cho found that the temperature outside had dropped a total of 35 degrees. Find the average change in temperature each day.
Solution:
We are given:
- Total change = –35 degrees (dropped)
- Number of days = 7
$$
\text{Average daily change} = \frac{-35}{7} = -5
$$
✔ Answer: The average change in temperature is
–5 degrees per day.
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4. BASKETBALL
Problem:
The basketball team lost their last 6 games. They lost by a total of 48 points. Find their average number of points relative to their opponents.
Solution:
We are given:
- Total point difference = –48 (they lost by 48 points overall)
- Number of games = 6
We want the
average point difference per game:
$$
\text{Average points relative to opponents} = \frac{-48}{6} = -8
$$
✔ Answer: The average number of points relative to their opponents is
–8 points per game.
> This means, on average, they scored 8 points less than their opponents in each game.
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✔ Final Answers Summary:
1.
Stock Market: –13 points per day
2.
Motion: –3 mph per second
3.
Weather: –5 degrees per day
4.
Basketball: –8 points per game
All problems use division to compute an
average rate of change over time or events.
Parent Tip: Review the logic above to help your child master the concept of dividing integers word problems worksheet.
