Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form.(1 point)
To subtract the expression 1/2(z+4) - 3(1/4z+1), we first distribute the -3 to both terms inside the parentheses:
1/2(z+4) - 3(1/4z+1) = 1/2(z+4) - (3/4z + 3)
Next, we can distribute the 1/2 to both terms inside the parentheses:
(1/2)z + (1/2)(4) - (3/4z + 3)
Simplifying further:
(1/2)z + 2/2 - (3/4z + 3)
Now, we need to find a common denominator between the fractions in order to combine them:
The common denominator is 4, so we need to multiply the numerator and denominator of (1/2) by 2 to get 4 as the denominator:
(2/4)z + 2/2 - (3/4z + 3)
Simplifying further:
(2/4)z + 1 - (3/4z + 3)
Now, combine like terms:
(2/4 - 3/4)z + (1 - 3)
Simplifying further:
(-1/4)z - 2
Thus, the expression 1/2(z+4) - 3(1/4z+1) in final form is (-1/4)z - 2.
To subtract the given expression, we need to distribute the numbers outside the parentheses.
First, let's distribute 1/2 to (z+4):
1/2 * (z+4) = (1/2)z + (1/2)4 = 1/2z + 2
Next, let's distribute -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 subtract these expressions, we need to have a common denominator, which is 4.
Multiplying the first term by 4/4 (which is essentially multiplying by 1) and the second term by 2/2 (which is also multiplying by 1) will give us the common denominator.
So,
(1/2z + 2)(4/4) - (3/4z + 3)(2/2)
= (4/8z + 8/4) - (6/4z + 6/2)
= 4/8z + 8/4 - 6/4z - 6/2
Now, let's combine like terms:
= (4z + 16)/8 - (6z + 12)/4
= (4z + 16)/8 - (3/2)(6z + 12)
= (4z + 16)/8 - (18z + 36)/8
Now, we can subtract the two terms:
= (4z + 16 - 18z - 36)/8
= (-14z - 20)/8
Our final answer is (-14z - 20)/8.
To subtract the given expression, 1/2(z+4) - 3(1/4z+1), we can use the distributive property of multiplication over addition/subtraction.
First, let's distribute 1/2 to (z+4):
1/2 * z = z/2
1/2 * 4 = 4/2 = 2
Hence, 1/2(z+4) becomes (z/2 + 2).
Next, let's distribute 3 to (1/4z+1):
3 * 1/4z = 3/4z
3 * 1 = 3
Hence, 3(1/4z+1) becomes (3/4z + 3).
Now, subtract (z/2 + 2) - (3/4z + 3):
In order to subtract the fractions, we need to find a common denominator. The common denominator for 2 and 4z is 4z.
(z/2) * (2z/2z) = z(2z)/4z = 2z^2/4z
2 * 4/2 = 8/2 = 4
Hence, (z/2 + 2) can be written as (2z^2/4z + 4).
(3/4z) * (4/4) = 12/16z
3 * 4 = 12
Hence, (3/4z + 3) can be written as (12/16z + 3).
Now, we can subtract (2z^2/4z + 4) - (12/16z + 3):
For the first fraction, the numerator and denominator are both divisible by 2, so we can simplify it further:
(2z^2/4z) = (z^2/2z).
Now, we can subtract the fractions:
(z^2/2z + 4) - (12/16z + 3)
To combine the fractions with a common denominator, we need to find the least common multiple (LCM) between 2z and 16z, which is 16z.
(z^2/2z) * (8/8) = 8z^2/16z
4 * 16 = 64
Hence, (z^2/2z) can be written as (8z^2/16z).
(12/16z) * (z/16) = 12z/256z
12 * 16 = 192
Hence, (12/16z) can be written as (12z/256z).
Now, we can subtract the fractions:
(8z^2/16z + 4) - (12z/256z + 3)
Combine the numerators:
(8z^2 + 4*16z) - (12z + 3*256z)
Simplify the terms:
(8z^2 + 64z) - (12z + 768z)
Combine like terms:
8z^2 + 64z - 12z - 768z
Simplify further:
8z^2 - 716z
Therefore, the final answer in fraction form is 8z^2 - 716z.