Question

( 14 + 2 ) 2 0 = 5 + 4 0 what type of property is this?

Answer 1

The question provides the relationship as shown below:

`((1)/(4)+2)20=5+40`

If we solve both sides individually, we have the left-hand side to give

`((1)/(4)+2)20=45`

and the right-hand side to give

`5+40=45`

Since both sides give the same result, we can attempt to manipulate the left-hand side of the equation with a common property we are familiar with: The Distributive Property.

The Distributive Property is written out as shown below:

`a(b+c)=(a\cdot b)+(a\cdot c)`

Applying this rule to the left-hand side, we get:

`\begin{gathered} ((1)/(4)+2)20=(1)/(4)\cdot20+2\cdot20 \\ =5+40 \end{gathered}`

This is the same expression present on the right-hand side of the equation.

Therefore, the property illustrated is the DISTRIBUTIVE PROPERTY.