Question

The model shows the expression 30 + 12.

A model with 6 rows of 5 squares and 6 rows of 2 squares.

Which expression is equivalent to this sum?
6 (5) + 2
6 + 5 + 2
6 + 5 (2)
6 (5 + 2)

Answer 1

To understand the given model, we can break it down as follows:

- The expression \( 30 + 12 \) can be interpreted in terms of the model with 6 rows.
- The model has two parts: 6 rows of 5 squares (which is \( 6 \times 5 = 30 \)) and 6 rows of 2 squares (which is \( 6 \times 2 = 12 \)).

Thus, the expression \( 30 + 12 \) can also be represented in a different way:

1. **Calculating the total number of squares:**
- Total squares = \( 30 + 12 = 42 \).

2. **Factoring using the common factor (6):**
- Both components can be expressed with the common factor of 6:
- The first part \( 30 \) can be rewritten as \( 6 \times 5 \).
- The second part \( 12 \) can be rewritten as \( 6 \times 2 \).
- Therefore, we can factor out the 6:
\[
30 + 12 = 6(5) + 6(2) = 6(5 + 2)
\]

From the options given:

- \( 6(5) + 2 \) is incorrect.
- \( 6 + 5 + 2 \) is incorrect.
- \( 6 + 5(2) \) is incorrect.
- **\( 6(5 + 2) \)** is correct.

So, the equivalent expression to the sum \( 30 + 12 \) in terms of the model is **\( 6(5 + 2) \)**.