Chapter 4.1, Problem 46PPS

To determine

To evaluate: $2\frac{2}{7}·14$ using distributive property

Answer to Problem 46PPS

  $32$

Explanation of Solution

Given information:

  $2\frac{2}{7}·14$

Concept Used:

Distributive Property: The product sum or difference of two or more numbers inside a parentheses with another number outside the parentheses is equivalent to the sum or difference of product of number outside the parentheses with each number inside the parenthesis. i.e.-

  $a\left(b+c-d\right)=ab+ac-ad$

Calculation:

We know $2\frac{2}{7}$ can be written as $2+\frac{2}{7}$

Therefore, the given expression can be written as-

  $\left(2+\frac{2}{7}\right)14$

We can write the given expression in distributive form as-

  $\left(2+\frac{2}{7}\right)14=\left(2\right)14+\left(\frac{2}{7}\right)14$

This can further be simplified as-

  $\begin{array}{l}\left(2\right)14+\left(\frac{2}{7}\right)14=28+\frac{28}{7}\\ \Rightarrow \left(2\right)14+\left(\frac{2}{7}\right)14=28+4\\ \Rightarrow \left(2\right)14+\left(\frac{2}{7}\right)14=32\end{array}$