Q78. - Algebra 1

Question

Explain why the multiplication property of equality and the division property of equality can be considered the same property. Which one do you think is easier to use?

Step-by-Step Solution

Answer

The Multiplication Property of Equality and the Division Property of Equality are considered as same.

Step 1. Given information.

Consider the Multiplication Property of Equality and the Division Property of Equality.

Step 2. Introduce the properties.

Consider, the explanation is to be done for the Multiplication Property of Equality and the Division Property of Equality as same.

Multiplication Property of Equality is the property that allows one multiply the same quantity by both sides of an equation.

Division Property of Equality is the property that allows one to divide the same quantity by both sides of an equation. Dividing by a number is the same as multiplying by the reciprocal, so the same rules would be applied.

Step 3. Write the example.

Consider an equation,

$\begin{array}{c}5x=35\\ \frac{5x}{5}=\frac{35}{5}\\ x=7\end{array}$

And, the number is multiplied by the reciprocal,

$\begin{array}{c}5x=35\\ \frac{1}{5}.5x=\frac{1}{5}.35\\ x=7\end{array}$

Step 4. Conclusion.

From the above shows that, the Multiplication Property of Equality and the Division Property of Equality are considered as same.

And, multiplication property is easier than Division Property.