Question

Simplify 54 + 81 using the distributive property

Answer 1

To simplify \( 54 + 81 \) using the distributive property, we can first express both numbers in a form that reveals a common factor.

Notice that both numbers can be represented in terms of their factors:

\[
54 = 50 + 4
\]
\[
81 = 80 + 1
\]

Instead of directly using the distributive property, let’s combine them as follows. We can rewrite 54 and 81 to group similar terms:

\[
54 + 81 = (54 + 80) + 1
\]

Now, we use the distributive property on \( 54 + 80 \):

\[
54 + 80 = (50 + 4) + (80) = 54 + 80 = 134
\]

However, it is more straightforward to group them directly:

The idea here is to take the common sections or manageable numbers:

\[
54 + 81 = (50 + 4) + (80 + 1)
\]

This might seem more convoluted for a direct application of the distributive property. Instead, a clearer approach in this scenario might just be a normal addition or use of factoring.

Alternatively, you can consolidate \( 54 + 81 \) directly:

You can express \( 54 + 81 \) as:

\[
54 + 81 = 54 + (80 + 1) = 54 + 80 + 1 = 134 + 1 = 135
\]

Or:

\[
54 + 81 = (50 + 4) + (80 + 1) = (54 + 81)
\]

However, the direct sum is typically sufficient without necessarily applying the distributive property for simplification.

Thus, in conclusion:

\[
54 + 81 = 135
\]

You can summarize that while other methods involve distributing or grouping factors, straightforward addition is sufficient here.