Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form
what is the answer
To subtract the expressions, let's expand and simplify each term separately:
First, let's expand 1/2(z + 4):
1/2(z + 4) = 1/2 * z + 1/2 * 4 = 1/2z + 2
Next, let's expand 3(1/4z + 1):
3(1/4z + 1) = 3 * 1/4z + 3 * 1 = 3/4z + 3
Now, let's subtract the two expressions:
1/2z + 2 - (3/4z + 3)
Next, let's get a common denominator for the fractions (which is 4):
1/2z + 2 - (3/4z + 3) = 1/2z + 2 - (3/4z + 3) * 2/2
Now, let's simplify the expression:
= 1/2z + 2 - (6/8z + 6/2)
= 1/2z + 2 - 6/8z - 3
Next, let's combine like terms:
= (1/2z - 6/8z) + (2 - 3)
= (4/8z - 6/8z) + (-1)
= (-2/8z) + (-1)
Now, let's simplify the expression further:
= -1/4z - 1
Therefore, the final simplified form of the expression is -1/4z - 1.
To subtract 1/2(z+4) - 3(1/4z+1), we need to distribute the coefficients inside 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 can subtract the terms:
(1/2z + 2) - (3/4z + 3)
To subtract fractions, we need a common denominator, which in this case is 4.
1/2z + 2 - (3/4z + 3) = 4/4 * (1/2z + 2) - (3/4z + 3)
= 4/8z + 8/4 - 3/4z - 12/4
= (4z - 3z) / 8 + (8 - 12) / 4
= z/8 - 4/4
Simplifying further,
z/8 - 4/4 = z/8 - 1
So, the final answer is z/8 - 1.
To subtract the given expression, we need to simplify and combine like terms. Let's start with the expression: 1/2(z+4) - 3(1/4z+1).
Step 1: Distribute 1/2 to (z+4):
1/2 * z = z/2
1/2 * 4 = 4/2 = 2
So, the expression becomes: (z/2 + 2) - 3(1/4z+1).
Step 2: Distribute 3 to (1/4z+1):
3 * 1/4z = 3/4z
3 * 1 = 3
So, the expression now becomes: (z/2 + 2) - (3/4z + 3).
Step 3: Combine like terms:
First, let's simplify (z/2 - 3/4z):
To add or subtract fractions, we need a common denominator. The least common multiple of 2 and 4 is 4, so we'll rewrite the fractions with a common denominator of 4:
(z/2) * (2/2) = (2z/4)
(3/4z) * (2/2) = (6/8z)
Now, the expression becomes: (2z/4 + 2) - (6/8z + 3).
Next, let's simplify (2z/4 + 6/8z):
To add or subtract fractions, we also need a common denominator. Here, the least common multiple of 4 and 8 is 8, so we'll multiply the first fraction by 2/2 and the second fraction by 1/2:
(2z/4) * (2/2) = (4z/8)
(6/8z) * (1/1) = (6/8z)
Now, the expression becomes: (4z/8 + 2) - (6/8z + 3).
Finally, combining like terms, we have:
(4z/8 - 6/8z) + (2 - 3)
= (4z - 6)/(8z) + (-1)
= (4z - 6)/(8z) - (1)/(1)
This is the final form of the expression subtracted using fractions.