Subtract 1/2 (z + 4) - 3 (1/4z +1). Use fractions in final form.
To solve this problem, we can distribute and simplify each term:
First, let's distribute and simplify the first term:
1/2 * z + 1/2 * 4 = 1/2 * z + 2 = z/2 + 2
Next, let's distribute and simplify the second term:
3 * 1/4z + 3 * 1 = 3/4z + 3
Now, let's subtract the two terms:
(z/2 + 2) - (3/4z + 3)
Next, let's find a common denominator for the fractions in the equation. The common denominator for 2 and 4 is 4. Multiply every term by 4 to get rid of the denominators:
(4 * z/2 + 4 * 2) - (4 * 3/4z + 4 * 3)
This simplifies to:
(2z + 8) - (3z + 12)
Now, let's expand the equation:
2z + 8 - 3z - 12
Combining like terms:
(2z - 3z) + (8 - 12) = -z - 4
Therefore, the final answer is -z - 4.
use fractions in final form
Sure, to write the final answer in fraction form, we can use the least common denominator approach. The least common denominator for the fractions involved is 4z.
Subtracting the fractions:
(1/2)z - (3/4)z + 4
To find a common denominator, multiply the numerator and denominator of the first fraction by 2 and the numerator and denominator of the second fraction by 4:
(2/4)z - (12/4)z + 4
Now, we can combine the fractions:
(2z - 12z) / 4z + 4
Simplifying the numerator:
(-10z) / 4z + 4
Now, let's simplify the denominator:
4z + 4
Therefore, the final answer is (-10z) / (4z + 4).
To subtract the given expression and simplify it using fractions, we will follow these steps:
Step 1: Distribute the terms within the parentheses.
Step 2: Combine like terms.
Step 3: Simplify the fractions if necessary.
Let's go through each step in detail:
Step 1: Distribute the terms within the parentheses.
Start with the expression: 1/2 (z + 4) - 3 (1/4z + 1)
Distribute 1/2 to (z + 4) and distribute -3 to (1/4z + 1):
1/2 * z + 1/2 * 4 - 3 * 1/4z - 3 * 1
This simplifies to:
1/2z + 2/2 - 3/4z - 3
Step 2: Combine like terms.
Now, combine the like terms together.
1/2z - 3/4z + 2/2 - 3
Step 3: Simplify the fractions if necessary.
To simplify the expression further, we need to make sure the fractions have the same denominator. The least common denominator (LCD) for 2 and 4 is 4.
Multiplying the numerator and denominator of 2/2 by 2, we get 4/4.
Now, simplifying the fractions:
(1/2 - 3/4)z + (4/4 - 3)
To subtract fractions, we need to have a common denominator. The LCD for 2 and 4 is 4.
So, 1/2 can be written as 2/4.
(2/4 - 3/4)z + (4/4 - 3)
Combining the fractions:
(-1/4)z + (1/4)
So, the final simplified expression, using fractions, is:
-1/4z + 1/4