ADD AND SUBTRACT ALGEBRAIC EXPRESSIONS PRACTICE
COMPLETE THIS ASSESSMENT TO REVIEW WHAT YOU'VE LEARNED. IT WILL NOT COUNT TOWARD YOUR GRADE.
Add:1/2 (x+4)+ 1/4 (4x-2). The answer should be in mixed number form
To solve this expression, we need to first distribute the fractions to their respective terms:
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 = x - 1/2
Now, we can add the two expressions:
(1/2x + 1) + (x - 1/2)
To combine like terms, we need to find a common denominator for the fractions:
The least common multiple of 2 and 4 is 4. So, we can rewrite the expression as:
(1/2x + 1) + (x - 2/4)
Now, to add the fractions, they must have a common denominator. We can convert 1 to 2/2:
(1/2x + 2/2) + (x - 2/4)
Simplifying further:
(1/2x + 2/2) + (x - 1/2)
Now, we combine the like terms:
1/2x + 2/2 + x - 1/2
To simplify, we need to find a common denominator again:
The least common multiple of 2 and 2 is 2. So, we can rewrite the expression as:
1/2x + 2/2 + 2x/2 - 1/2
Combining like terms:
(1/2x + 2x/2) + (2/2 - 1/2)
Simplifying:
1/2x + x/2 + 1/2
To add the fractions with a common denominator:
(1/2x + x/2) + 1/2
Now, we add the numerators:
(1x + x^2)/2x + 1/2
Combining the terms:
(x + x^2)/2x + 1/2
This is the final expression in mixed number form.