The model shows the expression 20 + 16.

A model with 4 rows of 5 squares and 4 rows of 4 squares.

Which expression is equivalent to this sum?
4 (5) + 4
4 + 5 + 4
4 (5 + 4)
5 (4 + 4)

1 answer

To analyze the expression \(20 + 16\) and the model described (which has 4 rows of 5 squares and 4 rows of 4 squares), we can interpret it as follows:

  • The model with 4 rows of 5 squares represents \(4 \times 5\), which equals 20.
  • The model with 4 rows of 4 squares represents \(4 \times 4\), which equals 16.

Combining these, we have: \[ 20 + 16 = 4 \times 5 + 4 \times 4 \]

This can be factored using the distributive property:

\[ = 4 \times (5 + 4) \]

Now, let's check the given options:

  1. \(4(5) + 4\) is not equivalent because it does not simplify to the original expression.
  2. \(4 + 5 + 4\) not equivalent to \(20 + 16\).
  3. \(4(5 + 4)\) is equivalent, as shown.
  4. \(5(4 + 4)\) also does not match.

Therefore, the expression that is equivalent to the sum \(20 + 16\) is: \[ \boxed{4(5 + 4)} \]