Illustrate an abstract mathematical concept showing two interconnected elements. The first element is a half division symbol, represented as a circular segment, with a vertical line at its right side. This element is linked to a lowercase 'b'. The second element depicts the letter 'b' enveloped by a semi-circular arc, suggesting division by two. Both these elements are connected by a plus symbol, floating in between. Keep the image text-less and appealing.

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.