The model shows the expression 21 + 9.

Question

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
7 (3 + 3)

Answer 1

To find an expression equivalent to the sum \(21 + 9\), let's analyze the information provided and the expressions listed.

1. Understanding the initial expression: \(21 + 9\) can be factored in a way that allows us to see a common expression.

   • \(21 = 3 \times 7\)
   • \(9 = 3 \times 3\)

2. Reformulation: If we add these together: \[ 21 + 9 = 3 \times 7 + 3 \times 3 \] This can also be factored to reveal: \[ 21 + 9 = 3(7 + 3) \] Thus, \(3(7 + 3)\) is equivalent to \(21 + 9\).

3. Evaluating the expressions:

   • \(3(7 + 3)\): This is already confirmed to be equivalent to the sum \(21 + 9\).
   • \(3(7) + 3\): This simplifies to \(21 + 3\), which equals \(24\). Not equivalent.
   • \(3 + 7 + 3\): This simplifies to \(13\). Not equivalent.
   • \(7(3 + 3)\): This simplifies to \(7 \times 6 = 42\). Not equivalent.

Thus, the expression that is equivalent to \(21 + 9\) is: \[ \boxed{3(7 + 3)} \]