add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed number form.(1 point)
To simplify the expression, we can first distribute the fractions:
1/2(x+4) + 1/4(4x-2)
= (1/2)x + (1/2)(4) + (1/4)(4x) + (1/4)(-2)
= (1/2)x + 2/2 + (4/4)x - 2/4
= (1/2)x + 1 + x - 1/2.
We can now combine like terms:
= (1/2)x + x + 1 - 1/2
= (3/2)x + 1 - 1/2.
To add the mixed number, we first need to find a common denominator for the fractions.
The common denominator for 2 and 1 is 2.
The common denominator for 2 and 1/2 is 2.
Now we can add the fractions:
= (3/2)x + (2/2) - (1/2)
= (3/2)x + (1/2).
Therefore, the simplified expression is (3/2)x + (1/2).
add: 1/2(x+4)+1/4 (4x-2). Answer should be in mixed number form.(1 point)
To simplify the expression, we can first distribute the fractions:
1/2(x + 4) + 1/4(4x - 2)
= (1/2)x + (1/2)(4) + (1/4)(4x) + (1/4)(-2)
= (1/2)x + 2/2 + (4/4)x - 2/4
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, we can add the whole numbers and fractions separately:
= (3/2)x + (1/2)
Since the coefficient in front of the variable, (3/2), is greater than 1, we can convert it to a mixed number.
To convert (3/2) to a mixed number, we divide the numerator (3) by the denominator (2). The quotient is the whole number, and the remainder is the numerator of the fraction:
3 ÷ 2 = 1 remainder 1
So, the mixed number form of (3/2) is 1 and 1/2.
Therefore, the simplified expression in mixed number form is:
1 and 1/2x + 1/2.
wrong
Apologies for the mistake. Let's go through the simplification again.
1/2(x+4) + 1/4(4x-2)
= (1/2)x + (1/2)(4) + (1/4)(4x) - (1/4)(2)
= (1/2)x + 2/2 + (4/4)x - 2/4
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, let's rewrite 1 as a fraction with a common denominator of 2:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 2/2 - 1/2
Now, we can add the fractions:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 1/2
Therefore, the simplified expression in mixed number form is:
1 and 1/2x.
To simplify the expression 1/2(x+4) + 1/4(4x-2), we will follow these steps:
Step 1: Distribute the 1/2 to the terms inside the parentheses:
1/2 * x + 1/2 * 4 = x/2 + 4/2
Step 2: Simplify the fractions:
x/2 + 4/2 = x/2 + 2
Step 3: Distribute the 1/4 to the terms inside the parentheses:
1/4 * 4x - 1/4 * 2 = 4x/4 - 2/4
Step 4: Simplify the fractions:
4x/4 - 2/4 = x - 1/2
Step 5: Add the two simplified terms together:
x/2 + 2 + x - 1/2
Step 6: Combine like terms:
(x + x)/2 + 2 - 1/2
Step 7: Combine the numerators of the fractions:
2x/2 + 4 - 1/2
Step 8: Simplify the fraction:
2x/2 + 4 - 1/2 = (2x + 4)/2 - 1/2 = (2x + 4 - 1)/2 = (2x + 3)/2
Thus, the answer in mixed number form is (2x + 3)/2.
To add the given expression, 1/2(x+4) and 1/4(4x-2), we can follow these steps:
Step 1: Distribute the coefficients inside 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 like terms.
(1/2)x + 2 + x - 1/2
Step 3: Find the LCD (Least Common Denominator) for the fractions present, which is 2.
Multiply the numerator and the denominator of the fraction (1/2) by 2 to obtain a common denominator.
(1/2)x + 2 + (2/2)(x) - 1/2 = (1/2)x + (2/2)x + 2 - 1/2
Step 4: Add the like terms.
(1/2)x + (2/2)x + 2 - 1/2 = (3/2)x + 2 - 1/2
Step 5: Subtract the fractions. Again, we need to find the LCD for 2 and 1.
Multiply the numerator and the denominator of the fraction (1/2) by 2 to obtain a common denominator.
(3/2)x + 2 - (1/2)(1) = (3/2)x + 2 - 1/2 = (3/2)x + (4/2) - (1/2) = (3/2)x + 3/2
The final answer, in mixed number form, is:
(3/2)x + 3/2