Question

Use the Properties of Identity, Inverse and Zero ,simplify$\frac{4}{7}+\frac{8}{15}+\left(-\frac{4}{7}\right)$

Short answer

The simplified form of$\frac{4}{7}+\frac{8}{15}+\left(-\frac{4}{7}\right)$is$\frac{8}{15}$

Step-by-step solution

Given information

Given expression is $\frac{4}{7}+\frac{8}{15}+\left(-\frac{4}{7}\right)$
.

Simplify the given expression Using additive identity .

Step 2:Description of additive identity

Additive identity:

For any real number $$\begin{gathered} a:a+0=a \\ 0+a=a \end{gathered}$$

0 is the additive identity.

Step 3:Simplification using additive identity

Here first and third terms are opposites, use the commutative Property of addition to re-order the terms.

$$\begin{gathered} \frac{4}{7}+\frac{8}{15}+\left(-\frac{4}{7}\right)=\frac{4}{7}+\left(-\frac{4}{7}\right)+\frac{8}{15} \\ =0+\frac{8}{15} \\ =\frac{8}{15},\sin ce0istheadditiveidentity. \end{gathered}$$