Question

choose the property of real numbers that justifies the equation.
$a + 4 = 4 + a$
select
$6\cdot(2\cdot m) = (6\cdot 2)\cdot m$
select
$\frac{1}{b}\cdot b = 1$
select
$n\cdot 0 = 0$
select

Explanation:

First Equation: \(a + 4 = 4 + a\)

Step1: Identify the property

The equation \(a + 4 = 4 + a\) shows that the order of adding \(a\) and \(4\) does not change the sum. This is the Commutative Property of Addition, which states that for any real numbers \(x\) and \(y\), \(x + y = y + x\).

Second Equation: \(6\cdot(2\cdot m)=(6\cdot 2)\cdot m\)

Step1: Identify the property

The equation \(6\cdot(2\cdot m)=(6\cdot 2)\cdot m\) shows that the way we group the factors \(6\), \(2\), and \(m\) when multiplying does not change the product. This is the Associative Property of Multiplication, which states that for any real numbers \(x\), \(y\), and \(z\), \(x\cdot(y\cdot z)=(x\cdot y)\cdot z\).

Third Equation: \(\frac{1}{b}\cdot b = 1\) (assuming \(b

eq0\))

Step1: Identify the property

The equation \(\frac{1}{b}\cdot b = 1\) shows that a number \(b\) (where \(b
eq0\)) multiplied by its reciprocal \(\frac{1}{b}\) gives \(1\). This is the Inverse Property of Multiplication, which states that for any non - zero real number \(x\), \(x\cdot\frac{1}{x}=1\) (where \(\frac{1}{x}\) is the multiplicative inverse of \(x\)).

Fourth Equation: \(n\cdot0 = 0\)

Answer:

s:

• For \(a + 4=4 + a\): Commutative Property of Addition
• For \(6\cdot(2\cdot m)=(6\cdot 2)\cdot m\): Associative Property of Multiplication
• For \(\frac{1}{b}\cdot b = 1\) (\(b

eq0\)): Inverse Property of Multiplication

• For \(n\cdot0 = 0\): Zero Property of Multiplication