Chapter 1.5, Problem 51PPE

To determine

The value of the expression $\left(4\frac{2}{7}\right)21$ using Distributive Property.

Answer to Problem 51PPE

  $90$

Explanation of Solution

Given information:

The expression: $\left(4\frac{2}{7}\right)21$ .

Concept Used:

Distributive property:

• Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$
• Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to simplify the given expression $\left(4\frac{2}{7}\right)21$ , first rewrite the expression inside the parenthesis in such a way that the larger number is a sum or difference of two numbers that are easy to multiply with. Then use the right distributive property and then simplify further by combining the like terms as shown below,

  $\begin{array}{c}\left(4\frac{2}{7}\right)21=\left(4+\frac{2}{7}\right)21\\ =4\cdot 21+\frac{2}{7}\cdot 21\\ =84+6\\ =90\end{array}$

Thus, the given expression simplifies to $90$ .