What is the sum start fraction 1 over 2b end fraction plus start fraction b over 2 end fraction ?
A. start fraction b plus 1 over 2b plus 2 end fraction
B. 2b
C. one-fourth
D. start fraction b superscript 2 baseline plus 1 over 2b end fraction
Well, well, well. It seems like you want to know the sum of start fraction 1 over 2b end fraction and start fraction b over 2 end fraction. Let me do some clown math for you.
To add these fractions, we need a common denominator. The smallest number that 2 and b can both divide evenly is 2b. So, let's rewrite the fractions with this common denominator.
The first fraction is start fraction b over 2 times (b/b) end fraction, which gives us start fraction b times b over 2b end fraction.
The second fraction is start fraction 1 over 2b times (2/2) end fraction, which gives us start fraction 1 times 2 over 2b end fraction.
Now, let's add these fractions together:
start fraction b times b over 2b end fraction plus start fraction 2 over 2b end fraction equals start fraction b times b plus 2 over 2b end fraction.
Ta-da! The sum is start fraction b superscript 2 baseline plus 2 over 2b end fraction. But wait, that's not one of the options you gave me! So the correct answer is D. start fraction b superscript 2 baseline plus 1 over 2b end fraction.
To find the sum of the fractions, we need to have a common denominator. In this case, the common denominator is 2b.
The first fraction is start fraction 1 over 2b end fraction, and the second fraction is start fraction b over 2 end fraction.
We need to rewrite these fractions with the common denominator of 2b:
start fraction 1 over 2b end fraction = start fraction b over 2b end fraction
start fraction b over 2 end fraction = start fraction b times b over 2 times b end fraction = start fraction b^2 over 2b^2 end fraction
Now, we can add the fractions together:
start fraction b over 2b end fraction + start fraction b^2 over 2b^2 end fraction = start fraction b^2 + 2b over 2b^2 end fraction
Therefore, the answer is D. start fraction b^2 + 2b over 2b^2 end fraction.
To solve this problem, we need to find the sum of the two fractions provided: start fraction 1 over 2b end fraction and start fraction b over 2 end fraction.
To add fractions, we need to first find a common denominator. In this case, the common denominator is 2b.
Now, let's rewrite the fractions with the common denominator: start fraction 1 over 2b end fraction + start fraction b over 2 end fraction = start fraction 1 times b over 2b times 1 end fraction + start fraction b times 2 over 2 times b end fraction
Simplifying the fractions, we get: start fraction b over 2b end fraction + start fraction 2b over 2b end fraction
Next, we add the fractions by adding the numerators together and keeping the common denominator: start fraction b + 2b over 2b end fraction = start fraction 3b over 2b end fraction
Finally, we can simplify the fraction by canceling out the common factor of b in the numerator and denominator: start fraction 3 over 2 end fraction
Therefore, the answer is option A: start fraction 3 over 2 end fraction, which is equivalent to start fraction b plus 1 over 2b plus 2 end fraction.
To add fractions, we need a common denominator. The smallest common multiple of 2 and b is 2b. So we can rewrite the expression as:
start fraction 1 over 2b end fraction plus start fraction b over 2 end fraction
= start fraction 1 times frac{b}{b} times frac{1}{2b} end fraction + start fraction 1 times frac{2}{2} times frac{b}{2b} end fraction
= start fraction b + 2b over 4b end fraction
= start fraction 3b over 4b end fraction
= start fraction 3}{4 end fraction b
Therefore, the answer is (A) start fraction b plus 1 over 2b plus 2 end fraction.