Question

For the following problem, match the name of the number property that was used to get to each step from the previous step.

Answer 1

Answer:

1) Given, 2) Inverse property of addition, 3) Commutative property/Identity property of addition, 4) Inverse property of multiplication, 5) Identity property of multiplication/Result.

Step-by-step explanation:

In this exercise we present what real number properties are used in each step of the given procedure with its respective explanations:

1) $37\cdot 2\cdot \left[(-5)+5+\frac{1}{2} \right]$ Given

2) $37\cdot 2\cdot \left(0+\frac{1}{2} \right)$ Inverse property of addition

The inverse property of addition states that:

$u + v = 0$, $\forall \,u, v \in \mathbb{R}$

$v = -u$

3) $37\cdot 2 \cdot \left(\frac{1}{2} \right)$ Commutative property/Identity property of addition

The commutative property of real numbers states that:

$u+v = v+u$, $\forall \,u,v\in\mathbb{R}$

The identity property of addition of real numbers states that:

$u+ 0 = u$, $\forall \,u\in\mathbb{R}$

4) $37\cdot 1$ Inverse property of multiplication.

The inverse property of real numbers states that:

$u\cdot v = 1$, $\forall\,u,v \in \mathbb{R}$

$v = u^{-1} = \frac{1}{u}$

5) $37$ Identity property of multiplication/Result.

The identity property of multiplication of real numbers states that:

$u\cdot 1 = u$, $\forall \,u\in \mathbb{R}$