Question

Evaluate each expression using properties of numbers. Name the property used in each step.

$7\frac{2}{5}+5+2\frac{3}{5}$

Short answer

The value of the given expression is $15$.

Step-by-step solution

Step 1. Commutative property of addition.

If $a$and $b$two integers then$a+b=b+a$

Step 2. Application of commutative property of addition.

$$\begin{gathered} 7\frac{2}{5}+5+2\frac{3}{5}=\frac{37}{5}+5+\frac{13}{5}\left[\mathrm{Converting}\mathrm{to}\mathrm{mixed}\mathrm{fraction}\right] \\ =\frac{37+13}{5}+5\left[\mathrm{Law}\mathrm{of}\mathrm{addition}\mathrm{of}\mathrm{fration}\right] \end{gathered}$$

Step 3. Simplifying the expression.

$$\begin{gathered} \frac{37+13}{5}+5=\frac{50}{5}+5\left[\mathrm{Substitution}\right] \\ =10+5\left[\mathrm{Substitution}\right] \\ =15\left[\mathrm{Substitution}\right] \end{gathered}$$