What is the sum
(1 / 2b) + (b / 2)
For those who need the answers:
1. A
2. D
3. C
4. C
5. D
100%
the common denominator is 2b, so you have
1/2b + b^2/2b
= (1+b^2)/2b
Well, if you're adding fractions, you need to find a common denominator. In this case, the common denominator is 2b. So, the first fraction becomes (1 * b) / (2b * b) = b / 2b². And the second fraction stays the same, b / 2. Now, we can add them together: (b / 2b²) + (b / 2). Let's not forget the cardinal rule of addition – we can only add things that are similar. So, we need to simplify the first fraction by canceling out the b in the numerator and denominator: 1 / 2b. Now we have (1 / 2b) + (b / 2). Adding these fractions with different denominators is like trying to dance the tango with a penguin – it just doesn't work. So, unfortunately, the sum of these two fractions cannot be simplified any further.
To find the sum of the fractions (1 / 2b) + (b / 2), we need to have a common denominator. In this case, the common denominator is 2b.
For the first fraction, we need to multiply both the numerator and the denominator by b to get the common denominator:
(1 / 2b) = b / (2b * b) = b / (2b^2)
For the second fraction, we need to multiply both the numerator and the denominator by 2:
(b / 2) = (b * 2) / (2 * 2) = (2b) / 4 = b / 2
Now that both fractions have the common denominator 2b, we can add them together:
(b / (2b^2)) + (b / 2)
To add these fractions, we need to have the same denominator: 2b^2.
For the second fraction, we need to multiply both the numerator and the denominator by b to get the common denominator:
(b / 2) = (b * b) / (2 * b) = b^2 / (2b)
Now the fractions have the same denominator, so we can add them together:
(b / (2b^2)) + (b^2 / (2b))
To add the fractions, we can combine the numerators and keep the denominator the same:
(b + b^2) / (2b^2)
Therefore, the sum of the fractions (1 / 2b) + (b / 2) is (b + b^2) / (2b^2).
To find the sum of (1 / 2b) + (b / 2), we need to combine the terms by finding a common denominator.
The denominators in the two terms are 2b and 2. To find a common denominator, we need to find the least common multiple (LCM) of these two numbers.
The LCM of 2b and 2 can be found by dividing their product by their greatest common divisor (GCD). In this case, the GCD of 2b and 2 is 2.
So, the LCM of 2b and 2 is (2b * 2) / 2 = 4b.
Now that we have a common denominator of 4b, we can rewrite the expression as follows:
(1 / 2b) + (b / 2) = [(1 * 2) / (2b * 2)] + [(b * 2b) / (2 * 2b)]
= (2 / 4b) + (2b^2 / 4b)
Since the denominators are now the same, we can simply add the numerators:
= (2 + 2b^2) / 4b
Therefore, the sum of (1 / 2b) + (b / 2) is (2 + 2b^2) / 4b.