Let's bring addition and subtraction together.
Solve each equation mentally.
$247 + c = 458$
$c + 43.87 = 58.92$
$\frac{15}{8} + c = \frac{51}{8}$
A mountaineer is changing elevations. Write an expression that represents the difference between the final elevation and beginning elevation. Then write the value of the change. The first one is done for you.
Mountaineer
Copyright Owner:
Orca
License:
Public Domain
Via:
Pixabay
| beginning elevation (feet) |
final elevation (feet) |
difference between final and beginning |
change | |
|---|---|---|---|---|
| row 1 | +400 | +900 | $900 - 400$ | +500 |
| row 2 | +400 | +50 | ||
| row 3 | +400 | -120 | ||
| row 4 | -200 | +610 | ||
| row 5 | -200 | -50 | ||
| row 6 | -200 | -500 | ||
| row 7 | -200 | 0 |
Fill in the table so that every row and every column sums to 0. Can you find another way to solve this puzzle?
| -12 | 0 | 5 | ||
| 0 | -18 | 25 | ||
| 25 | -18 | 5 | -12 | |
| -12 | -18 | |||
| -18 | 25 | -12 |
| -12 | 0 | 5 | ||
| 0 | -18 | 25 | ||
| 25 | -18 | 5 | -12 | |
| -12 | -18 | |||
| -18 | 25 | -12 |
| A | B | |
|---|---|---|
| row 1 | $3 - 2$ | $2 - 3$ |
| row 2 | $5 - (\text-9)$ | $(\text-9) - 5$ |
| row 3 | $(\text-11) - 2$ | $2 - (\text-11)$ |
| row 4 | $(\text-6) - (\text-3)$ | $(\text-3) - (\text-6)$ |
| row 5 | $(\text-1.2) - (-3.6)$ | $(\text-3.6) - (\text-1.2)$ |
| row 6 | $(\text-2\frac12) - (\text-3\frac12)$ | $(\text-3\frac12) - (\text-2\frac12)$ |
When we talk about the difference of two numbers, we mean, “subtract them.” Usually, we subtract them in the order they are named. For example, the difference of +8 and $\text-6$ is $8 - (\text-6)$.
The difference of two numbers tells you how far apart they are on the number line. 8 and -6 are 14 units apart, because $8 - (\text-6) = 14$:
Notice that if you subtract them in the opposite order, you get the opposite number:
$$(\text-6)-8 = \text-14$$
In general, the distance between two numbers $a$ and $b$ on the number line is $|a - b|$. 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.
