Subtract 1/2(z+4)−3(1/4z+1) . Use fractions in final form. pls show answer
To subtract fractions, we need to find a common denominator. In this case, the common denominator will be 4.
1/2(z+4) - 3(1/4z+1)
Multiply the first fraction by 4/4 and the second fraction by 2/2 to get the common denominator:
= (4/4)(1/2)(z+4) - (3/4)(2/2)(1/4z+1)
Simplify the fractions:
= (4/8)(z+4) - (6/8)(1/4z+1)
= (1/2)(z+4) - (3/4)(z/4 + 1)
Distribute the fractions:
= (1/2)(z) + (1/2)(4) - (3/4)(z/4) - (3/4)(1)
= (z/2) + 2/2 - 3z/16 - 3/4
Combine like terms:
= z/2 + 1 - 3z/16 - 3/4
To add or subtract fractions, we must have the same denominator. The least common denominator (LCD) is 16, so we need to convert the fractions accordingly:
= (8z/16) + (16/16) - (3z/16) - (12/16)
Combine like terms:
= (8z - 3z) / 16 + (16 - 12) / 16
= 5z/16 + 4/16
= (5z + 4) / 16
Therefore, the final answer is (5z + 4) / 16.
To subtract the given expression, 1/2(z+4) - 3(1/4z+1), we need to simplify and combine like terms. Let's break down the steps:
Step 1: Distribute the coefficients.
Distribute the 3 to both terms inside the parentheses:
1/2(z+4) - (3)*(1/4z + 1)
= 1/2(z) + 1/2(4) - 3*(1/4z) - 3*(1)
= 1/2z + 2/2 - 3/4z - 3
Step 2: Simplify the fractions on each term.
Combine 1/2z and -3/4z by finding a common denominator, which is 4.
(4)*(1/2z) = 4/2z = 2z
(4)*(3/4z) = 12/4z = 3z
The expression becomes:
2z + 2/2 - 3z - 3
Step 3: Simplify the remaining fractions and combine like terms.
2/2 equals 1, so the expression further simplifies to:
2z + 1 - 3z - 3
Step 4: Combine like terms.
Combine 2z and -3z, which gives -z. Then combine 1 and -3, which gives -2.
The final answer is:
-z - 2
So, the simplified form of 1/2(z+4) - 3(1/4z+1) is -z - 2.
To subtract 1/2(z+4)−3(1/4z+1), we need to first distribute the coefficients outside the parenthesis.
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 two expressions:
1/2z + 2 - (3/4z + 3)
To combine like terms, we need to find a common denominator, which in this case is 4:
(1/2z * 4/4) + (2 * 4/4) - (3/4z + 3)
= 4/8z + 8/4 - 3/4z - 3
Now we can combine like terms:
(4z + 16 - 3z - 12) / 8z
= (4z - 3z + 16 - 12) / 8z
= (z + 4) / 8z
The final answer in fraction form is (z + 4) / 8z.