Chapter 7.1, Problem 32IP

To determine

The value of the expression $10\cdot 5\frac{1}{2}$ using Distributive Property.

Answer to Problem 32IP

  $55$

Explanation of Solution

Given information:

The expression: $10\cdot 5\frac{1}{2}$ .

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 $10\cdot 5\frac{1}{2}$ , first $5\frac{1}{2}$ can written as $5+\frac{1}{2}$ and then using the left distributive property and then simplify further as shown below,

  $\begin{array}{c}10\cdot 5\frac{1}{2}=10\cdot \left(5+\frac{1}{2}\right)\\ =10\cdot 5+10\cdot \frac{1}{2}\\ =50+5\\ =55\end{array}$

Thus, the given expression simplifies to $55$ .