
Concept explainers
When asked to compare the sizes of two numbers, most people think of subtraction, but the example above shows that this isn’t necessarily the best choice. The difference between two values is found by simply subtracting the new value from the old:
Difference =
New value – Old value
In both scenarios above, the difference in what was owed and what was paid is $10, which leads us to conclude the significance of that $10 is the same in each case. But doesn’t it seem clear that the $10 shortfall is more significant when the total amount owed is $20? That’s where relative difference comes in. The relative difference between two values measures the difference as a fraction of the original value.
Relative difference=DifferenceOriginal value=New value-OriginalvalueOriginalvalue
In Scenario 1 above:
Relative difference =$10−$20$20=−12 or –50%. (The negative indicates that you got shorted. Bummer.))
This shows that the difference between the amount owed and the amount received is half of the amount owed. That’s a big deal!
Both Shawna and John found out that they’re getting a $1,000 annual raise this year. John went out to celebrate, while Shawna yawned and said “Yeah, whatever.” Use the topic of this section to describe what you think might be likely to account for this discrepancy in their reactions to the news.

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Chapter 2 Solutions
Pathways to Math Literacy (Loose Leaf)
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