The model shows the expression 30 + 12.

Question

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 \( 6(5 + 2) \).