The question provides the relationship as shown below:
[tex](\frac{1}{4}+2)20=5+40[/tex]
If we solve both sides individually, we have the left-hand side to give
[tex](\frac{1}{4}+2)20=45[/tex]
and the right-hand side to give
[tex]5+40=45[/tex]
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:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]
Applying this rule to the left-hand side, we get:
[tex]\begin{gathered} (\frac{1}{4}+2)20=\frac{1}{4}\cdot20+2\cdot20 \\ =5+40 \end{gathered}[/tex]
This is the same expression present on the right-hand side of the equation.
Therefore, the property illustrated is the DISTRIBUTIVE PROPERTY.
