1/2 ( x + 4) + 1/4 (4x - 2) as mixed numbers
To simplify the expression 1/2 ( x + 4) + 1/4 (4x - 2), we can first simplify each term separately and then combine them.
1/2 ( x + 4) = (1/2)x + (1/2)(4) = (1/2)x + 2
1/4 (4x - 2) = (1/4)(4x) - (1/4)(2) = x - 1/2
Now we can combine the two simplified terms:
(1/2)x + 2 + x - 1/2
To combine these terms, we need to have a common denominator. The least common denominator between 2 and 4 is 4. So we can rewrite the expression as:
(2/4)x + 2 + (2/4)x - 1/2
Simplifying further:
(2x/4) + 2 + (2x/4) - 1/2
= (2x + 2 + 2x) / 4 - 1/2
= (4x + 2)/4 - 1/2
Now, let's write it as a mixed number. To do this, we divide the numerator by the denominator:
(4x + 2)/4 = (4x/4) + (2/4) = x + 1/2
So, the expression 1/2 ( x + 4) + 1/4 (4x - 2) simplifies to x + 1/2.
To convert the given expression into mixed numbers, we will first simplify the expression by performing the operations involved.
Step 1: Distribute the fractions.
1/2 (x + 4) + 1/4 (4x - 2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Step 2: Simplify each term.
= 1/2 * x + 2/2 + 4/4 * x - 2/4
Step 3: Combine like terms.
= 1/2 * x + 1 + 1 * x - 1/2
Step 4: Combine the x terms.
= (1/2 + 1) * x + (1 - 1/2)
Step 5: Simplify the coefficients.
= 3/2 * x + 1/2
Therefore, the expression 1/2 (x + 4) + 1/4 (4x - 2) can be written as the mixed numbers 3/2x + 1/2.
To convert the given expression into mixed numbers, follow these steps:
Step 1: Expand the brackets
Expand the first bracket (1/2) (x + 4) and the second bracket (1/4) (4x - 2).
(1/2) (x + 4) = (1/2) * x + (1/2) * 4 = (1/2) x + 2
(1/4) (4x - 2) = (1/4) * 4x + (1/4) * -2 = x - 1/2
Step 2: Simplify the expression
Combine the like terms in the equation.
(1/2) x + 2 + x - (1/2) = (1/2) x + x + 2 - (1/2) = (3/2) x + 2 - (1/2) = (3/2) x + 1 1/2
Therefore, the given expression, 1/2 ( x + 4) + 1/4 (4x - 2), can be written as a mixed number (3/2) x + 1 1/2.