Chapter 4.1, Problem 38PPS

To determine

To evaluate: $31·11$

Answer to Problem 38PPS

  $341$

Explanation of Solution

Given information:

  $31·11$

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:

  $31·11=341$

We can also solve it using distributive property.

  $31$ can be written as $30+1$

The expression $31·11$ will now become

  $\left(30+1\right)11$

We can write the given expression in distributive form as-

  $\left(30+1\right)11=\left(30\right)11+\left(1\right)11$

This can further be evaluated as-

  $\begin{array}{l}\left(30\right)11+\left(1\right)11=330+11\\ \Rightarrow \left(30\right)11+\left(1\right)11=341\end{array}$

Both the answers match