Add: 1/2(x + 4) + 1/4(4x - 2). Answer should be in mixed number form
To add the fractions, we first need to find a common denominator. The least common multiple of 2 and 4 is 4. So, we can rewrite the fractions as:
1/2(x + 4) = (1/2)(2/2)(x + 4) = (x + 4)/4
1/4(4x - 2) = (1/4)(4/4)(4x - 2) = (4x - 2)/4
Now, we can add the fractions:
(x + 4)/4 + (4x - 2)/4 = (x + 4 + 4x - 2)/4 = (5x + 2)/4
To express this in mixed number form, we divide the numerator (5x + 2) by the denominator (4) and write the remainder over the denominator. The quotient becomes the whole number part, and the remainder becomes the fractional part.
The whole number part is given by the division: 5x ÷ 4 = 5/4 x = 1 and 1/4.
Therefore, the sum 1/2(x + 4) + 1/4(4x - 2) in mixed number form is 1 and 1/4.
Wrong
Apologies for the previous incorrect response. Let's redo the calculation.
1/2(x + 4) + 1/4(4x - 2)
First, let's distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplifying each term:
(x/2) + 2/2 + (4x/4) - 2/4
Now, let's combine like terms:
(x/2) + 1 + x - 1/2
Next, we need to find a common denominator:
2(x/2) + 2(1/2) + 2(x/2) - 1/2
Simplifying further:
2x/2 + 2/2 + 2x/2 - 1/2
Adding the numerators across:
(2x + 2 + 2x - 1)/2
Now, combine like terms:
(4x + 1)/2
To express this in mixed number form, we divide the numerator (4x + 1) by the denominator (2) and write the remainder over the denominator. The quotient becomes the whole number part, and the remainder becomes the fractional part.
The whole number part is given by the division: (4x + 1) ÷ 2 = 2x + 1/2.
Therefore, the sum 1/2(x + 4) + 1/4(4x - 2) in mixed number form is 2x + 1/2.
To add the given expression and simplify the answer into mixed number form, follow these steps:
Step 1: Distribute the coefficients to the terms within each parentheses.
1/2(x + 4) becomes 1/2 * x + 1/2 * 4 = 1/2x + 2
1/4(4x - 2) becomes 1/4 * 4x + 1/4 * -2 = x - 1/2
Step 2: Combine the like terms by adding the coefficients of similar variables.
1/2x + 2 + x - 1/2
Step 3: Add the whole numbers separately and the fractions separately.
2 + (-1/2) = 1 1/2
Step 4: Add the coefficients of "x" terms.
1/2x + x = 3/2x
Step 5: Combine the whole number and the fraction, and write the answer in mixed number form.
Therefore, the final answer is 1 1/2 + 3/2x.