Q13. - Algebra 1

Question

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

$\mathbf{2}\left(3\cdot 2-5\right)\mathbf{+}\mathbf{3}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{2}\left(3\cdot 2-5\right)\mathbf{+}\mathbf{3}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{3}}\mathbf{=}\mathbf{3}$

Step 1 – Given information.

Given expression is:

$2\left(3\cdot 2-5\right)+3\cdot \frac{1}{3}$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

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

The multiplicative inverse is:

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

The multiplicative identity is:

$a\times 1=a$

Step 3 – Evaluate the expression.

The expression $2\left(3\cdot 2-5\right)+3\cdot \frac{1}{3}$ can be solved in below:

$\begin{array}{c}2\left(3\cdot 2-5\right)+3\cdot \frac{1}{3}=2\left(3\cdot 2-5\right)+1\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}multiplicative inverse}\right]\\ =2\left(6-5\right)+1\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =2\left(1\right)+1\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =2+1\left[\text{Property of Mulplication\hspace{0.17em}\hspace{0.17em}Identity}\right]\\ =3\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$