Q14. - Algebra 1

Question

Evaluate the following expression. Name the property used in each step:

$\mathbf{6}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{6}}\mathbf{+}\mathbf{5}\left(12÷4-3\right)$

Step-by-Step Solution

Answer

The value of the expression is: .$\mathbf{6}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{6}}\mathbf{+}\mathbf{5}\left(12÷4-3\right)\mathbf{=}\mathbf{1}$

Step 1 – Given information.

Given expression is:

$6\cdot \frac{1}{6}+5\left(12÷4-3\right)$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a÷b=c\\ a\pm b=c\end{array}$

The multiplicative inverse is:

$a\times \frac{1}{a}=1$

The property of multiplicative of any number to 0 is:

$a\times 0=0$

The Additive inverse is:

$a+\left(-a\right)=0$

Step 3 – Evaluate the expression.

The expression $6\cdot \frac{1}{6}+5\left(12÷4-3\right)$ can be solved in below:

$\begin{array}{c}6\cdot \frac{1}{6}+5\left(12÷4-3\right)=1+5\left(12÷4-3\right)\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}multiplicative inverse}\right]\\ =1+5\left(3-3\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =1+5\left(0\right)\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}additive\hspace{0.17em}\hspace{0.17em}inverse}\right]\\ =1+0\left[\text{Property of Mulplication\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}zero}\right]\\ =1\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$