Q1. - Algebra 1

Question

Name the property used in each step:

$\begin{array}{c}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(4\cdot 2-8\right)\mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(8-8\right)\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(0\right)\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{6}\mathbf{+}\mathbf{0}\mathbf{\text{ \_\_\_\_\_\_}}\\ \mathbf{=}\mathbf{6}\mathbf{\text{ \_\_\_\_\_\_}}\end{array}$

Step-by-Step Solution

Answer

$\begin{array}{c}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(4\cdot 2-8\right)\mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(8-8\right)\underset{\mathbf{¯}}{\mathbf{\text{Substitution}}}\mathbf{4}\mathbf{\cdot }\mathbf{2}\mathbf{=}\mathbf{8}\\ \mathbf{=}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{+}\left(0\right)\underset{\mathbf{¯}}{\mathbf{\text{Substitution}}}\mathbf{8}\mathbf{-}\mathbf{8}\mathbf{=}\mathbf{0}\\ \mathbf{=}\mathbf{6}\mathbf{+}\mathbf{0}\underset{\mathbf{¯}}{\mathbf{\text{Substitution}}}\mathbf{2}\mathbf{\cdot }\mathbf{3}\mathbf{=}\mathbf{6}\\ \mathbf{=}\mathbf{6}\underset{\mathbf{¯}}{\mathbf{\text{Substitution}}}\mathbf{6}\mathbf{+}\mathbf{0}\mathbf{=}\mathbf{6}\end{array}$

Step 1 – Given information.

Given expression is:

$\begin{array}{c}2\cdot 3+\left(4\cdot 2-8\right)=2\cdot 3+\left(8-8\right)\text{ \_\_\_\_\_\_}\\ =2\cdot 3+\left(0\right)\text{ \_\_\_\_\_\_}\\ =6+0\text{ \_\_\_\_\_\_}\\ =6\text{ \_\_\_\_\_\_}\end{array}$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

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

Step 3 – Write the property.

Since,

$\begin{array}{c}2\cdot 3+\left(4\cdot 2-8\right)=2\cdot 3+\left(8-8\right)\text{ \_\_\_\_\_\_}\\ =2\cdot 3+\left(0\right)\text{ \_\_\_\_\_\_}\\ =6+0\text{ \_\_\_\_\_\_}\\ =6\text{ \_\_\_\_\_\_}\end{array}$

In 1^st step,

$4\cdot 2=8$ (Substitution Property)

In 2^nd step,

$\left(8-8\right)=0$ (Substitution Property)

In 3^rd step,

$2\cdot 3=6$ (Substitution Property)

In 4^th step,

$6+0=6$ (Substitution Property)