Q33. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

The value of the given expression is $15$.

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.

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