Add: 1/2(r+4)+1/4(4r-2). Answer should be in mixed number form
To simplify the expression, let's first distribute the fractions:
1/2(r+4) + 1/4(4r-2) = (1/2*r + 1/2*4) + (1/4*4r - 1/4*2)
Simplifying further:
= 1/2r + 2/2 + 1r - 1/2
= 1/2r + 2/2 + 1r - 1/2
= (1/2r + 1r) + (2/2 - 1/2)
= 3/2r + 1/2
Now, let's convert the improper fraction 3/2r into mixed number form.
3/2r = 1 + 1/2r
So the final answer in mixed number form is: 1 + 1/2r
wrong
To add the terms, first simplify each fraction:
1/2(r + 4) = (r + 4)/2
1/4(4r - 2) = (4r - 2)/4
Now, let's find a common denominator to add the fractions. The least common denominator (LCD) is 4:
(r + 4)/2 = (r + 4)(2/2) = (2r + 8)/4
(4r - 2)/4 = (4r - 2)(1/1) = (4r - 2)/4
Now, add the fractions:
(2r + 8)/4 + (4r - 2)/4 = (2r + 4r + 8 - 2)/4 = (6r + 6)/4
Finally, simplify the fraction if possible:
(6r + 6)/4 = 6(r + 1)/4 = 6/4 * (r + 1) = (1 2/4) * (r + 1)
The answer in mixed number form is (1 2/4)(r + 1).
To add the given expression, 1/2(r + 4) + 1/4(4r - 2), we need to find a common denominator for the fractions involved.
First, let's work on the expression 1/2(r + 4):
To distribute the 1/2 to the terms in the parentheses (r + 4), we multiply each term by 1/2:
1/2 * r = 1/2r
1/2 * 4 = 2
So, 1/2(r + 4) simplifies to (1/2r) + 2.
Now, let's work on the expression 1/4(4r - 2):
To distribute the 1/4 to the terms in the parentheses (4r - 2), we multiply each term by 1/4:
1/4 * 4r = r
1/4 * -2 = -1/2
So, 1/4(4r - 2) simplifies to r - 1/2.
Now, let's add the simplified expressions (1/2r + 2) and (r - 1/2):
(1/2r + 2) + (r - 1/2) =
To combine the terms with 'r', we can add the coefficients:
1/2r + r = 3/2r
To combine the constant terms, we can add the coefficients:
2 + (-1/2) = 4/2 - 1/2 = 3/2
Therefore, (1/2r + 2) + (r - 1/2) simplifies to (3/2r) + (3/2).
To express the answer in mixed number form, we divide the numerator (3) by the denominator (2), which gives us a quotient of 1 and a remainder of 1. Therefore, the final answer in mixed number form is:
1 1/2 + 3/2 = 2 1/2
Apologies for the earlier mistake. Let's correct it.
1/2(r+4) + 1/4(4r-2)
First, let's distribute the fractions:
= 1/2 * r + 1/2 * 4 + 1/4 * 4r - 1/4 * 2
= 1/2r + 2/2 + 1r - 1/2
Now, let's simplify:
= 1/2r + 1 + 1r - 1/2
Combining like terms:
= 1r + 1/2r + 1 - 1/2
= (2r + 1)/(2r) + 2/2 - 1/2
= (2r + 1)/(2r) + 1/2 - 1/2
= (2r + 1)/(2r)
The final answer in mixed number form is 2r + 1 over 2r.