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) [tex]37\cdot 2\cdot \left[(-5)+5+\frac{1}{2} \right][/tex] Given
2) [tex]37\cdot 2\cdot \left(0+\frac{1}{2} \right)[/tex] Inverse property of addition
The inverse property of addition states that:
[tex]u + v = 0[/tex], [tex]\forall \,u, v \in \mathbb{R}[/tex]
[tex]v = -u[/tex]
3) [tex]37\cdot 2 \cdot \left(\frac{1}{2} \right)[/tex] Commutative property/Identity property of addition
The commutative property of real numbers states that:
[tex]u+v = v+u[/tex], [tex]\forall \,u,v\in\mathbb{R}[/tex]
The identity property of addition of real numbers states that:
[tex]u+ 0 = u[/tex], [tex]\forall \,u\in\mathbb{R}[/tex]
4) [tex]37\cdot 1[/tex] Inverse property of multiplication.
The inverse property of real numbers states that:
[tex]u\cdot v = 1[/tex], [tex]\forall\,u,v \in \mathbb{R}[/tex]
[tex]v = u^{-1} = \frac{1}{u}[/tex]
5) [tex]37[/tex] Identity property of multiplication/Result.
The identity property of multiplication of real numbers states that:
[tex]u\cdot 1 = u[/tex], [tex]\forall \,u\in \mathbb{R}[/tex]
