1/2 (x + 4) + 1/4 (4x - 2)
answer should be in mixed number form
To find the sum, we need to simplify the expression:
1/2 (x + 4) + 1/4 (4x - 2)
First, distribute 1/2 to (x + 4):
1/2 * x = (1/2)x
1/2 * 4 = 2
So we have:
(1/2)x + 2 + 1/4(4x - 2)
Now distribute 1/4 to (4x - 2):
1/4 * 4x = x
1/4 * -2 = -1/2
So now the expression becomes:
(1/2)x + 2 + x - 1/2
Combine like terms:
(1/2)x + x + 2 - 1/2
Now we can add the x terms and the constant terms separately:
(1/2)x + x = (3/2)x
2 - 1/2 = 3/2
Putting it all together:
(3/2)x + 3/2
In mixed number form, this is:
1 1/2x + 1 1/2
(4d - 3) + (12d + 4)
To find the sum, we need to simplify the expression:
(4d - 3) + (12d + 4)
We can remove the parentheses first:
4d - 3 + 12d + 4
Now, let's combine like terms:
(4d + 12d) + (-3 + 4)
This simplifies to:
16d + 1
The answer in mixed number form is:
16d + 1
(2m - 3) + (3n - 1) + (3m + 1)
To find the sum, we need to simplify the expression:
(2m - 3) + (3n - 1) + (3m + 1)
We can remove the parentheses first:
2m - 3 + 3n - 1 + 3m + 1
Now, let's combine like terms:
(2m + 3m) + (-3 - 1) + (3n + 1)
This simplifies to:
5m - 4 + 3n + 1
Let's further simplify the constants:
5m + 3n - 3
The answer in mixed number form is:
5m + 3n - 3
To simplify the given expression, follow these steps:
Step 1: Distribute the fractions
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Step 2: Combine like terms
= 1/2 * x + 2 + 4/4 * x - 1/2
Step 3: Simplify fractions
= 1/2 * x + 2 + 1 * x - 1/2
Step 4: Combine like terms
= (1/2x + x) + (2 - 1/2)
= 3/2x + 3/2
Therefore, the simplified expression is 3/2x + 3/2 in mixed number form.
To solve the expression 1/2 (x + 4) + 1/4 (4x - 2) and obtain the answer in mixed number form, we need to simplify the expression by combining like terms.
Step 1: Distribute the coefficients to the terms within the parentheses.
Distributing 1/2 to (x + 4) gives us (1/2) * x + (1/2) * 4 = 1/2x + 2
Distributing 1/4 to (4x - 2) gives us (1/4) * 4x + (1/4) * (-2) = x - 1/2
Step 2: Combine like terms.
Combining 1/2x and x gives us (1/2x + x) = (3/2)x
Combining 2 and -1/2 gives us (2 + (-1/2)) = 3/2
Therefore, the simplified expression is (3/2)x + 3/2.
To write the answer in mixed number form, we need to convert the improper fraction 3/2 into a mixed number.
Step 3: Divide the numerator (3) by the denominator (2).
3 ÷ 2 = 1 remainder 1.
The quotient (integer part) is 1, and the remainder (numerator) is 1.
Hence, the final answer in mixed number form is 1 and 1/2.