Subtract 1/2(z+4)−3(1/4z+1). Use fractions in final form.
To subtract the given expression, we need to distribute the coefficients to their respective terms.
First, distribute the 1/2 to (z+4):
1/2 * (z+4) = (1/2)*(z) + (1/2)*(4) = 1/2z + 2
Next, distribute the -3 to (1/4z+1):
-3 * (1/4z+1) = (-3)*(1/4z) + (-3)*(1) = -3/4z - 3
Now we can subtract the two terms:
1/2z + 2 - 3/4z - 3
To simplify this expression, we need to find a common denominator for the fractions. The common denominator is 4, so we multiply the first term by 2/2 and the second term by 4/4:
(1/2)*(z/1)*(2/2z) + 2*(2/2) - (3/4z)*(4/4) - 3*(4/4)
This gives us:
(2z/4z) + 4/2 + (-12/4z) - 12/4
Simplifying each term:
(2z + 4) - (3z) - 3
Combining like terms:
2z - 3z + 4 - 3
Simplifying again:
-z + 1
So the final simplified form of the expression is -z + 1 in fraction form.
To subtract 1/2(z+4)−3(1/4z+1), we need to distribute and simplify the expression.
Step 1: Distribute the 1/2 to (z+4):
1/2 * z + 1/2 * 4 = 1/2z + 2
Step 2: Distribute the -3 to (1/4z+1):
-3 * 1/4z + -3 * 1 = -3/4z - 3
Now we have:
1/2z + 2 - 3/4z - 3
Step 3: Combine like terms:
(1/2z - 3/4z) + (2 - 3) = 1/2z - 3/4z - 1
To simplify, we need to find a common denominator for the fractions 1/2z and 3/4z. The common denominator is 4:
(2z/4) - (3z/4) - 1 = (2z - 3z)/4 - 1
Step 4: Combine the numerator terms:
(-z)/4 - 1
Therefore, the final simplified expression is -z/4 - 1.
To subtract the given expression: 1/2(z + 4) - 3(1/4z + 1), we need to simplify each term and then combine them.
Step 1: Distribute the coefficients outside the parentheses:
1/2(z + 4) = (1/2 * z) + (1/2 * 4) = 1/2z + 2
3(1/4z + 1) = 3 * (1/4z) + 3 * 1 = 3/4z + 3
Now we have: 1/2z + 2 - 3/4z - 3
Step 2: Combine like terms. We have two terms with z and two constant terms:
(1/2z - 3/4z) + (2 - 3)
To combine the fractions, we need to find a common denominator:
The common denominator for 2 and 4 is 4. So we need to convert 1/2z to have a denominator of 4:
(1/2z * 2/2) - 3/4z + 2 - 3
This gives us: 2/4z - 3/4z - 1
Step 3: Combine the z terms and the constant terms:
(2/4z - 3/4z) - 1 = (2 - 3)/4z - 1 = -1/4z - 1
Therefore, the final result after simplifying and expressing the answer in fractional form is: -1/4z - 1.