Add: 1/2 (x+4) + 1/4 (4x−2) . The answer should be in mixed number form
To simplify the expression 1/2 (x+4) + 1/4 (4x−2), we first need to distribute the coefficients:
(1/2) * (x + 4) = (1/2)x + (1/2)4 = 1/2x + 2
(1/4) * (4x - 2) = (1/4)4x + (1/4)(-2) = x - 1/2
Therefore, the simplified expression is:
1/2x + 2 + x - 1/2
We can combine the like terms by adding the coefficients of x together:
1/2x + x = (1/2 + 1)x = (3/2)x
And combining the constant terms together:
2 - 1/2 = 4/2 - 1/2 = 3/2
So the final simplified expression is:
(3/2)x + 3/2
To write this in mixed number form, we convert the improper fraction to a mixed number. The numerator of 3/2 is greater than the denominator, so we divide the numerator by the denominator:
3 ÷ 2 = 1 remainder 1
Therefore, the mixed number form of the expression is:
1 and 1/2x + 3/2
To add the fractions (1/2)(x+4) and (1/4)(4x−2), follow these steps:
Step 1: Distribute the coefficients to the terms in the parentheses.
(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 + x + 1/2 − 1/2
Step 4: Convert the coefficients to a common denominator.
= (2/2)x + (2/2)x + 1/2 − 1/2
Step 5: Simplify the expression.
= (4/2)x
= 2x
Therefore, the simplified expression is 2x, and it is already in mixed number form.
To add the given expression, 1/2(x+4) + 1/4(4x-2), we'll start by simplifying the individual terms.
For 1/2(x+4), we can distribute the 1/2 to each term inside the parentheses:
1/2(x+4) = (1/2) * x + (1/2) * 4
Simplifying further:
= 1/2x + 2/2
= 1/2x + 1
Next, let's simplify the term 1/4(4x-2) in a similar manner:
1/4(4x-2) = (1/4) * 4x + (1/4) * (-2)
Simplifying further:
= 1x - 1/2
= x - 1/2
Now, we can combine the two simplified terms:
(1/2x + 1) + (x - 1/2)
To add these two terms, we need a common denominator. In this case, the smallest common denominator is 2:
= (1/2x + 1) + (2x/2 - 1/2)
Now, we can add the numerators together:
= (1 + 2x)/2x + (2x - 1)/2
Combining the fractions:
= (1 + 2x + 2x - 1)/2x
Simplifying the numerator:
= (4x)/2x
The x terms in the numerator and denominator cancel out:
= 4/2
Finally, we can simplify the fraction:
= 2
Therefore, the answer in mixed number form is 2.