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Which three go together? Why do they go together?
A
B
C
D
The scoring margin tells how many points a sports team wins a game by.
Here are the scoring margins for one football team for the season.
Here are the scoring margins for another football team for the season.
What was this team’s average scoring margin for the season?
A family has solar panels on their roof to help generate electricity.
Calculate the family’s net consumption of electricity for each of these days:
When the solar panels generate more electricity than the family can use, their energy company gives them a credit for the extra electricity that goes back to the power grid. Here is their electricity bill for one month:
| Amount used: | 520.0 kWh | \$83.20 |
|---|---|---|
| Amount generated: | -143.5 kWh | -\$11.48 |
| Amount due: | $71.72 |
The family adds a backup battery to their solar panel system. Here is their energy usage for a new month. Calculate their amount due to the energy company this month.
| Amount used: | 164.5 kWh | |
|---|---|---|
| Amount generated: | -203.0 kWh | |
| Amount due: |
We can apply the rules for arithmetic with rational numbers to solve problems.
In general, .
If , then . We can add to both sides of this second equation to get that .
Remember: The distance between two numbers is independent of the order, while the difference depends on the order.
And when multiplying or dividing:
A positive number multiplied or divided by a negative number always has a negative result.
A negative number multiplied or divided by a positive number always has a negative result.
A negative number multiplied or divided by a negative number always has a positive result.