Which pictorial model is equivalent to the expression 4(5+2)?
a. | 5 | 2 |
b. | 4 | 5 | 2 |
| 4 | 5 | 2 |
| 4 | 5 | 2 |
| 4 | 5 | 2 |
c. | 4 | 5 | 2 |
d. | 5 | 2 | 5 | 2 |
To determine which pictorial model is equivalent to the expression 4(5+2), you need to understand the order of operations in mathematics. The expression follows the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
In this case, the expression is being multiplied by 4. To represent multiplication, we need to repeat the pictorial model of the expression being multiplied.
Now let's break down the expression 4(5+2):
1. Start with the expression inside the parentheses: 5+2 = 7.
2. Multiply 7 by 4 to get the final result: 7 * 4 = 28.
Let's analyze the given options:
a. Option (a) is not equivalent since it represents 5 + 2 instead of 4(5+2).
b. Option (b) consists of multiple repetitions of the expression 5+2, but it does not multiply the entire expression by 4. Therefore, it is not equivalent.
c. Option (c) represents the expression as 4 | 5 | 2 with vertical lines. This model correctly represents multiplication of the entire expression by 4, so it is a valid representation.
d. Option (d) represents two separate instances of 5 and 2, without any multiplication. Therefore, it is not equivalent.
From the given options, the pictorial model that is equivalent to the expression 4(5+2) is option (c).