add:1/2(x+4)+1/4(4x-2) answer in mixed number
To solve this equation and present the answer as a mixed number, we need to simplify the expression first.
1/2(x+4) + 1/4(4x-2)
Using the distributive property, we can distribute the fractions:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= (1/2)x + 2/2 + (4/4)x - 2/4
Simplifying the fractions, we have:
= (1/2)x + 1 + x - 1/2
Now, let's combine like terms:
= (1/2)x + x - 1/2 + 1
= (3/2)x - 1/2 + 2/2
= (3/2)x + 1/2
The equation in fraction form is (3/2)x + 1/2.
To present it as a mixed number, we can convert the fraction into a mixed number. The fraction (3/2) can be expressed as 1 1/2.
Thus, the answer in mixed number form is 1 1/2x + 1/2.
To add the given expression, we need to combine like terms. Let's simplify step by step:
1/2(x+4) + 1/4(4x-2)
First, distribute 1/2 to (x+4):
1/2 * x + 1/2 * 4 = 1/2x + 2
Next, distribute 1/4 to (4x-2):
1/4 * 4x - 1/4 * 2 = x - 1/2
Now, we have:
1/2x + 2 + x - 1/2
Combine the like terms:
(1/2x + x) + (2 - 1/2)
Adding x and 1/2x, we get 3/2x:
3/2x + 2 - 1/2
To combine 2 and -1/2, we need a common denominator of 2:
2 = 4/2
Now, we can rewrite the expression:
(3/2x) + (4/2 - 1/2)
Combine 4/2 and -1/2:
4/2 - 1/2 = 3/2
Finally, the simplified expression is:
3/2x + 3/2
To convert the improper fraction to a mixed number, we divide the numerator (3) by the denominator (2):
3 ÷ 2 = 1 remainder 1
Therefore, the final answer is:
1 1/2x + 3/2
To solve the given expression and convert it into a mixed number, you'll need to follow these steps:
Step 1: Simplify the given expression
Start by distributing the fractions to their respective terms inside the parentheses:
1/2(x+4) + 1/4(4x-2)
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
(1/2 * x) + (2/2) + (4/4 * x) - (2/4)
Now, simplify the fractions:
x/2 + 2/2 + x - 1/2
Combine like terms:
x/2 + 2/2 + x - 1/2 = (x + 2 + 2x - 1) / 2
= (3x + 1) / 2
Step 2: Convert the fraction to a mixed number
To convert the fraction (3x + 1) / 2 into a mixed number, divide the numerator by the denominator:
(3x + 1) ÷ 2
The quotient will be the whole number part, and the remainder will be the numerator of the fraction part.
For example, if x = 5:
(3 * 5 + 1) ÷ 2 = 16 ÷ 2 = 8
The quotient is 8, so the whole number part is 8.
Now we calculate the remainder:
(3 * 5 + 1) % 2 = 16 % 2 = 0
The remainder is 0, which means there is no fraction part.
Therefore, the final mixed number is 8.
In summary, the expression 1/2(x+4) + 1/4(4x-2) simplifies to (3x + 1) / 2, and when evaluated with a specific value for x (e.g., x = 5), the solution is the mixed number 8.