Question

find the result graphically in three different ways, using the commutative property of addition. click and drag the arrows to represent each term. type in the common result. \\(-5 - 4 + 7\\)

Explanation:

Step1: Rewrite using commutative property

First rearrangement: $-5 + 7 - 4$
Second rearrangement: $7 - 5 - 4$
Third rearrangement: $7 - 4 - 5$

Step2: Calculate the original expression

$$\begin{align*} -5 - 4 + 7 &= (-5 - 4) + 7 \\ &= -9 + 7 \\ &= -2 \end{align*}$$

Step3: Verify rearrangements

1. $-5 + 7 - 4 = 2 - 4 = -2$
2. $7 - 5 - 4 = 2 - 4 = -2$
3. $7 - 4 - 5 = 3 - 5 = -2$

For number line representation (each version):

1. For $-5 - 4 + 7$: Start at 0, move left 5 units to $-5$, move left 4 units to $-9$, move right 7 units to $-2$.
2. For $-5 + 7 - 4$: Start at 0, move left 5 units to $-5$, move right 7 units to $2$, move left 4 units to $-2$.
3. For $7 - 5 - 4$: Start at 0, move right 7 units to $7$, move left 5 units to $2$, move left 4 units to $-2$.

Answer:

The common result is $\boldsymbol{-2}$
The three equivalent expressions are:

1. $-5 + 7 - 4$
2. $7 - 5 - 4$
3. $7 - 4 - 5$

Each expression graphs to the point $-2$ on the number line.