Question

The model shows the expression 21 + 9.

A model with 3 rows of 7 squares and 3 rows of 3 squares.

Which expression is equivalent to this sum?
3 (7 + 3)
3 (7) + 3
3 + 7 + 3

Answer 1

The expression \(21 + 9\) can be analyzed in the context of the model described.

You have:
- 3 rows of 7 squares, which represent \(3 \times 7 = 21\).
- 3 rows of 3 squares, which represent \(3 \times 3 = 9\).

So, the total is:
\[ 21 + 9 = 3 \times 7 + 3 \times 3 \]

This shows the sum as \(3 (7) + 3 (3)\).

Now, looking at the options you provided:

1. \(3 (7 + 3)\) = \(3 \times 10 = 30\) (not equivalent)
2. \(3 (7) + 3\) = \(21 + 3 = 24\) (not equivalent)
3. \(3 + 7 + 3 = 13\) (not equivalent)

The decision of which expression is equivalent to \(21 + 9\) can actually be simplified to the form \(3 (7) + 3 (3)\), which matches what we deduced.

None of the expressions provided directly match \(21 + 9\). However, if you rewrite \(3(7 + 3)\) to its expanded form, it leads you nor to the result properly.

Thus, none of the provided options are equivalent to the original expression \(21 + 9\) based on how you described the model setup. However, the expression \(3(7) + 3(3)\) which isn't listed would yield the correct representation.

In conclusion, since none of the options work, reinterpretation reveals the necessary expression is \(3(7) + 9\). The correct reflection of the given would still be the observation that no option given reflects \(21 + 9\) as noted directly from the modeling perspective.