When you’re writing expressions to represent real-world situations, remember that expressions can have more than one operation. That’s when things can get a little tricky. Some operations are commutative. That means changing the order of the terms will not change the answer. Addition and multiplication are commutative. When adding the terms 4 and 3n, we can say 4 + 3n or 3n + 4.
Which of these two expressions represent the phrase “five plus two times a number”?
A
5n + 2n and 2n + 5n
B
5 + 2n and 2 + 5n
C
2n + 5 and 2n - 5
D
5 + 2n and 2n + 5
The expression that represents the phrase "five plus two times a number" is D) 5 + 2n and 2n + 5.
you can only pick one
In that case, the correct answer would be D) 5 + 2n and 2n + 5.
To determine which expression represents the phrase "five plus two times a number," we need to understand the order of operations.
According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition. This means that when we have the phrase "two times a number," we need to perform the multiplication first.
Now, let's examine the given options:
A) 5n + 2n and 2n + 5n
B) 5 + 2n and 2 + 5n
C) 2n + 5 and 2n - 5
D) 5 + 2n and 2n + 5
Looking at option B, we notice that the multiplication (2 times a number) comes after the addition (5 plus 2n). This is incorrect since multiplication should be performed before addition.
Option D, however, correctly represents the phrase "five plus two times a number." It follows the correct order of operations: first, we multiply 2 and n, and then we add 5 to the result.
Therefore, the correct answer is D) 5 + 2n and 2n + 5.