Which expression is equivalent to sum of negative four and one half times n plus the quantity one fourth plus one and three fourths times n minus three eighths?
negative eleven fourths times n plus five eighths
negative eleven fourths times n minus one eighth
negative twenty five fourths times n minus one eighth
negative twenty five fourths times n plus one eighth
To simplify the expression, we distribute the multiplication:
-4 * (1/2 * n) + (1/4 + 1 + 3/4) * n - 3/8
-2/2 * n + (2/4 + 4/4 + 6/4) * n - 3/8
-n + (12/4) * n - 3/8
-n + 3n - 3/8
Now combine like terms:
(-n + 3n) - 3/8
2n - 3/8
Therefore, the equivalent expression is: negative twenty five fourths times n plus one eighth
To find the equivalent expression, we need to simplify the given expression step by step.
The given expression is:
-4 + 1/2n + (1/4 + 1 3/4n - 3/8)
Let's simplify it step by step:
1. Combine the fractions within the parentheses:
1/4 + 1 3/4n - 3/8
To combine the fractions, we need to find a common denominator, which in this case is 8.
1/4 + 1 3/4n - 3/8
= 2/8 + 1 6/8n - 3/8
= 1 6/8n - 1/8
The expression now becomes:
-4 + 1/2n + (1 6/8n - 1/8)
2. Distribute the 1/2 to n within the parentheses:
1/2n + 1 6/8n - 1/8
Multiplying 1/2 by n gives us 1/2n.
The expression now becomes:
-4 + 1/2n + 1 6/8n - 1/8
3. Combine like terms:
The like terms are the n terms.
1/2n + 6/8n
To combine these, we need to find a common denominator, which is 8.
4/8n + 6/8n
= 10/8n
Simplifying this further, we get:
= 5/4n
The expression now becomes:
-4 + 5/4n - 1/8
4. Combine the constants:
-4 - 1/8
To combine these, we need to find a common denominator, which is 8.
-32/8 - 1/8
= -33/8
The expression now becomes:
-33/8 + 5/4n
Therefore, the equivalent expression is:
negative thirty-three eighths plus five fourths times n, which is represented as:
negative thirty-three eighths plus five fourths times n.
The correct answer is: negative thirty-three eighths plus five fourths times n
To simplify the given expression, let's break it down step by step:
The expression is: sum of negative four and one half times n plus the quantity one fourth plus one and three fourths times n minus three eighths.
Step 1:
Rewrite "negative four and one half" as a fraction.
Negative four and one half can be written as -4 1/2, which is equivalent to -4 - 1/2 = -8/2 - 1/2 = -9/2.
Step 2:
Combine like terms for the first part of the expression.
The first part of the expression is -9/2 times n.
Step 3:
Combine the second part of the expression.
The second part of the expression is the quantity one fourth plus one and three fourths times n minus three eighths.
Let's simplify this part:
- One fourth plus one and three fourths is equal to (1/4) + (1 + 3/4) = (1/4) + (4/4) + (3/4) = 8/4 = 2.
- So, the second part of the expression becomes 2n - 3/8.
Step 4:
Combine both parts of the expression.
The entire expression becomes -9/2 times n + 2n - 3/8.
Step 5:
Combine the terms with n.
-9/2 times n + 2n = -9n/2 + 2n = (-9n + 4n)/2 = -5n/2.
Step 6:
Combine the remaining terms.
The entire expression becomes -5n/2 - 3/8.
So, the expression is equivalent to (-5n/2) - (3/8).
Now, let's compare this expression to the provided options:
- Negative eleven fourths times n plus five eighths: -11/4n + 5/8
- Negative eleven fourths times n minus one eighth: -11/4n - 1/8
- Negative twenty-five fourths times n minus one eighth: -25/4n - 1/8
- Negative twenty-five fourths times n plus one eighth: -25/4n + 1/8
From the simplified expression (-5n/2) - (3/8), it matches the option "negative twenty five fourths times n minus one eighth."
So, the answer is:
The expression is equivalent to negative twenty-five fourths times n minus one eighth.