Subtract 1/2 (z+4)−3(1/4 z+1) . Use fractions in final form.(1 point)
To subtract 1/2 (z+4) - 3(1/4z+1), we need to distribute the coefficients and combine like terms.
First, distribute 1/2 to z and 4:
1/2 * z + 1/2 * 4 = 1/2z + 2
Second, distribute -3/4 to z and 1:
-3/4 * z - 3/4 * 1 = -3/4z - 3/4
Now, let's put the terms together:
1/2z + 2 - 3/4z - 3/4
To combine like terms, we need to find a common denominator for the fractions. The common denominator in this case is 4.
Rewriting the fractions with the common denominator:
(1/2z - 3/4z) + (2 - 3/4)
Simplifying:
-1/4z + 8/4 - 3/4
Combining like terms:
-1/4z + (8-3)/4
Simplifying further:
-1/4z + 5/4
Therefore, the simplified form of 1/2 (z+4) - 3(1/4z+1) is -1/4z + 5/4.
To subtract the expression 1/2(z+4) - 3(1/4z+1), we need to simplify each term separately and then combine like terms.
1/2(z+4) can be expanded by distributing the 1/2 across the terms inside the parentheses:
1/2(z) + 1/2(4) = 1/2z + 2
3(1/4z+1) can be expanded similarly by distributing the 3 across the terms inside the parentheses:
3(1/4z) + 3(1) = 3/4z + 3
Now, we can subtract the two expressions:
(1/2z + 2) - (3/4z + 3)
To combine like terms, we need to have the same denominator for the z terms (1/2z and 3/4z). The least common denominator (LCD) for 2 and 4 is 4. We can convert 1/2 to 2/4 by multiplying the numerator and denominator by 2:
(2/4z + 2) - (3/4z + 3)
Now, we can subtract the expressions:
(2/4z - 3/4z) + (2 - 3)
When subtracting the z terms, the denominator (4) remains the same. The numerator is subtracted:
(2-3)/4z + (2-3) = -1/4z - 1
So, the final answer is -1/4z - 1.
To subtract the given expression, follow these steps:
Step 1: Simplify each term within the parentheses.
(a) Simplify 1/2(z+4):
To do this, distribute the 1/2 to both terms inside the parentheses:
1/2 * z = z/2
1/2 * 4 = 4/2 = 2
Therefore, 1/2(z+4) simplifies to (z/2 + 2).
(b) Simplify 3(1/4 z+1):
Distribute the 3 to both terms inside the parentheses:
3 * 1/4z = 3/4z
3 * 1 = 3
Therefore, 3(1/4 z+1) simplifies to (3/4z + 3).
Step 2: Combine like terms.
Now that both terms are simplified, we can subtract them:
(z/2 + 2) - (3/4z + 3)
To subtract these fractions, you need to find a common denominator. In this case, the common denominator is 4z.
Multiply the first fraction by 4z/4z:
[(z/2)(4z)]/4z + (2(4z))/4z
This simplifies to (4z^2/8z) + (8z/4z).
Multiply the second fraction by 2/2:
(3/4z)(2/2) + (3(2))/2
This simplifies to (6/8z) + (6/2).
Combine the numerators and keep the common denominator:
(4z^2 + 8z + 6)/(8z).
Therefore, Subtracting 1/2(z+4)−3(1/4 z+1) and using fractions in final form, the result is (4z^2 + 8z + 6)/(8z).