Q6. - Algebra 1

Question

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

$\mathbf{2}\mathbf{.75}\mathbf{+}\mathbf{3}\mathbf{.5}\mathbf{+}\mathbf{4}\mathbf{.25}\mathbf{+}\mathbf{1}\mathbf{.5}$

Step-by-Step Solution

Answer

The value of the expression is: $\mathbf{2}\mathbf{.75}\mathbf{+}\mathbf{3}\mathbf{.5}\mathbf{+}\mathbf{4}\mathbf{.25}\mathbf{+}\mathbf{1}\mathbf{.5}\mathbf{=}\mathbf{12}$.

Step 1 – Given information.

Given expression is:

$2.75+3.5+4.25+1.5$

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 commutative property of addition is:

$a+b=b+a$

Step 3 – Evaluate the expression.

The expression $2.75+3.5+4.25+1.5$ can be solved in below:

$\begin{array}{c}2.75+3.5+4.25+1.5=\left(2.75+4.25\right)+\left(3.5+1.5\right)\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(7\right)+\left(5\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =12\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$