QuestionShow on a number line that $-4+3$ and $3+(-4)$ are equal. What addition property proves this?

Studdy Solution

STEP 1

Assumptions1. The number line is a visual representation of numbers in order. . The operation of addition is commutative, which means the order of the numbers does not change the result.
3. The operation of addition with negative numbers is the same as subtraction.

STEP 2

First, let's represent the operation $-4+$ on a number line. We start at -4 on the number line.
$Start\, at\, -4$

STEP 3

Then, we move3 units to the right, which represents adding3.
$Move\,3\, units\, to\, the\, right$

STEP 4

The position we end up at on the number line represents the result of the operation $-4+3$ .
$End\, at\, -1$

STEP 5

Now, let's represent the operation $3+(-4)$ on a number line. We start at3 on the number line.
$Start\, at\,3$

STEP 6

Then, we move4 units to the left, which represents adding -4 (or subtracting4).
$Move\,4\, units\, to\, the\, left$

STEP 7

The position we end up at on the number line represents the result of the operation $3+(-4)$ .
$End\, at\, -1$

STEP 8

By comparing the results of the two operations on the number line, we can see that they both end up at the same position, -1. This shows that $-4+3$ and $3+(-4)$ have the same value.
$-4+3 =3+(-4) = -1$

STEP 9

The property of addition that states that these sums are equivalent is the Commutative Property of Addition. It states that changing the order of the addends does not change the sum.
$Commutative\, Property\, of\, Addition a+b = b+a$ In this case, $-4+3$ is the same as $3+(-4)$ , which is a demonstration of the Commutative Property of Addition.

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