Chapter 1.4, Problem 42IP

To determine

Translate the verbal expression into an algebraic expression, then simplify it, the product of seven and four times a number multiplied by three.

Answer to Problem 42IP

  $\left(7\times 4x\right)\times 3;84x$

Explanation of Solution

Given:

The product of seven and four times a number multiplied by three.

Concept Used:

Associative property of multiplication

  $a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$

In order to translate the verbal expression into an algebraic expression, then simplify it, the product of seven and four times a number multiplied by three, first let the number be x then the product of seven and four times a nymber implies seven multiply 4 times x and then multiplying by 3, so the expression is as shown below:

  $\left(7\times 4x\right)\times 3$

Now, simplify the above equation by using associative property of multiplication as shown below:

  $\begin{array}{l}\left(7\times 4x\right)\times 3\\ =4x\times \left(7\times 3\right)\\ =4x\times \left(21\right)\\ =84x\end{array}$

So, the algebraic expression is $\left(7\times 4x\right)\times 3$ , and the simplification is 84x.