Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number
To simplify the given expression and express the answer in a mixed number, we will first distribute the fractions:
1/2(x+4) + 1/4(4x−2)
1/2 * x + 1/2 * 4 + 1/4 * 4x − 1/4 * 2
x/2 + 2/2 + 4x/4 − 2/4
Next, we will combine like terms:
x/2 + 2/2 + 4x/4 − 2/4
x/2 + 1 + x − 1/2
x/2 + x/2 + 1 − 1/2
2x/2 + 1/2 − 1/2
(2x + 1)/2
Thus, the simplified expression is (2x + 1)/2, which cannot be expressed as a mixed number.
make it a mixed number
Apologies for the confusion. Since the expression (2x + 1)/2 cannot be expressed as a mixed number, there is no way to rewrite it in that form.
To add the given expression, follow these steps:
Step 1: Simplify the expressions within the parentheses:
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: Combine the simplified expressions:
(1/2)x + 2 + x - 1/2
Step 3: Combine like terms:
(1/2)x + x + 2 - 1/2
Step 4: Add the coefficients of 'x':
(1/2 + 1)x + 2 - 1/2 = (3/2)x + 2 - 1/2
Step 5: Simplify the constants:
2 - 1/2 = 4/2 - 1/2 = 3/2
Step 6: Combine the results:
(3/2)x + 3/2 = (3/2)x + 1 and 1/2
Therefore, the given expression, 1/2(x+4) + 1/4(4x−2), simplifies to (3/2)x + 1 and 1/2 in mixed number form.
To add the given expression and express the answer as a mixed number, we can follow these steps:
Step 1: Distribute the coefficients.
Apply the distributive property to each term inside the parentheses:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1
1/4(4x−2) = 1/4 * 4x - 1/4 * 2 = 4/4x - 2/4 = 1x - 1/2
Simplifying, we have:
1/2(x+4) + 1/4(4x−2) = 1/2x + 1 + 1x - 1/2
Step 2: Combine like terms.
The like terms here are the x-term and the constant terms. Combine them:
1/2x + 1 + 1x - 1/2 = 1/2x + 1x + 1 - 1/2
Step 3: Find a common denominator.
To add fractions, we need to express them with a common denominator. In this case, the lowest common denominator (LCD) is 2.
So, we need to convert 1/2x to a fraction with a denominator of 2.
Multiplying both the numerator and denominator of 1/2x by 2, we get:
(1/2)(2/2x) = 2/4x = 1/2x
Step 4: Combine the terms and simplify.
Now that all the fractions have a common denominator of 2, we can add the fractions:
1/2x + 1x + 1 - 1/2 = (1/2x) + (2/2x) + 1 - 1/2
Combine the x-terms:
(1/2x) + (2/2x) = (1 + 2)/2x = 3/2x
The expression now becomes:
3/2x + 1 - 1/2
Combine the constant terms:
1 - 1/2 = 2/2 - 1/2 = 1/2
So, the final expression is:
3/2x + 1/2
To express it as a mixed number, we divide the numerator by the denominator:
(3/2) ÷ (1/2) = 3 ÷ 1 = 3
The remainder is 0 since 3 is evenly divisible by 1.
Therefore, the answer is 3 as a mixed number.