Chapter 1.4, Problem 37PPE

To determine

Whether the expressions are equivalent or not.

Answer to Problem 37PPE

The given expressions are equivalent.

Explanation of Solution

Given information:

Given expressions are,

  $\left(30+17\right)\times 10$ and $\left(10\times 30\right)+\left(10\times 17\right)$

Calculation:

Two expressions are said to be equivalent if there values obtained same. To represent equivalent expression an equality = sign is used.

Check equivalent expression,

Take Left hand side

  $\begin{array}{c}\left(30+17\right)\times 10=47\times 10\\ =470\end{array}$

Now Right hand side

  $\begin{array}{c}\left(10\times 30\right)+\left(10\times 17\right)=300+170\\ =470\end{array}$

Hence, Left hand side equal to Right hand side.

So, this expression is equivalent.

Here, distributive property of real numbers has been used.