Add:1/2 (x+4)+ 1/4 (4x-2). Answer should be in mixed number form
To solve the given expression and express the answer in mixed number form, we need to simplify the expression by combining like terms.
1/2 (x+4) + 1/4 (4x-2)
First, let's distribute the coefficients:
= (1/2)x + (1/2)x + 2 + (-1/2)
Combining like terms:
= (1/2)x + (1/2)x + 2 - 1/2
= x + x + 2 - 1/2
= 2x + 2 - 1/2
Next, let's find a common denominator to subtract the fractions:
= 2x + 2 - 1/2
Since 2/2 equals 1, we can rewrite 1/2 as 2/4:
= 2x + 2 - 2/4
Now, we can subtract the fractions:
= 2x + 2 - 2/4
= 2x + 2 - 1/2
Since 2 can be written as 4/2, we can change the whole number 2 to a fraction:
= 2x + 4/2 - 1/2
Now that we have a common denominator, we can combine the fractions:
= 2x + 4/2 - 1/2
= 2x + 3/2
Finally, we can express the answer in mixed number form. A mixed number consists of a whole number and a proper fraction. To convert a fraction into mixed number form, we divide the numerator by the denominator:
= 2x + 3/2
First, let's divide 3 by 2:
3 ÷ 2 = 1 remainder 1
So the mixed number form is:
= 2x + 1 1/2
Therefore, the simplified expression in mixed number form is 2x + 1 1/2.