Unit 7, Lesson 10
Finding Differences
Accelerated 6
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A mountaineer is changing elevations. The table shows some beginning and final elevations.
| beginning elevation (feet) |
final elevation (feet) |
difference between final and beginning |
change (feet) |
|---|---|---|---|
| +400 | +900 | +500 | |
| +400 | +50 | ||
| +400 | -120 | ||
| -200 | +610 | ||
| -200 | -50 | ||
| -200 | -500 | ||
| -200 | 0 |
For each row of the table:
To find the difference between two numbers, we subtract them. Usually, we subtract them in the order they are named. For example, “the difference of +8 and -6” means . We can find the value of by thinking . Representing this on a number line, we can see that the second arrow must be 14 units long, pointing to the right.
A number line with the numbers negative 10 through 10, indicated. An arrow starts at 0, points to the left, ends at negative 6, and is labeled "minus 6". A second arrow starts at negative 6, points to the right, ends at 8, and is labeled "plus 14". There is a solid dot at 8.
The difference of two numbers tells us how far apart they are on the number line and in which direction. The difference of +8 and -6 is 14 because these numbers are 14 units apart, and 8 is to the right of -6.
A number line with the numbers negative 10 through 10 indicated. Two solid dots are on the number line located at, negative 6 and 8. An arrow starts at negative 6, points to the right, ends at 8, and is labeled "positive 14."
If we subtract the same numbers in the opposite order, we get the opposite number. For example, “the difference of -6 and +8” means . This difference is -14 because these numbers are 14 units apart, and -6 is to the left of +8.
A number line with the numbers negative 10 through 10 indicated. Two solid dots are on the number line located at, negative 6 and 8. An arrow starts at 8, points to the left, ends at negative 6, and is labeled "negative 14."
In general, the distance between two numbers and on the number line is . Note that the distance between two numbers is always positive, no matter the order. But the difference can be positive or negative, depending on the order.