Answer Within A Minute III

Simplify the 1st fraction denominator with the 2nd fraction numerator for example $\frac{1}{3}$ with $\frac{3}{5}$ to become $\frac{1}{5}$ and do it continuously until the last. The final answer will be $\frac{1}{49} = \frac{a}{b}$ . Therefore, a+b = 1+49 = 50

The given expression immediately simplifies to $\frac{1}{49}$ , so a+b=50.

We can easily see that denominator of the 1st fraction and numerator of the second fraction are same so they will omit each other and in the last fraction since there is no other fractions numerator to omit its denominator so it will remain and the numerator will be omitted by the previous fraction denominator that is 1/49 will remain that is a=1 and b=19.So a+b=50

If look carefully at problem then we get that denominater and numerator of other gets cancelled ans. 1/49 .49+1=50

All the values are canceled from each other in the end we have remain just 1 and 49 so a+b like 1+49=50 so simple :)

Let's answer by seeing the first five fractions.

$\frac {1}{3} * \frac {3}{5} * \frac {5}{7} * \frac {7}{9} * \frac {9}{11} * \ldots * \frac {47}{49}$

Do you see how you can cross-multiply ? Look again.

$\frac {1}{3} * \frac {3}{5} = \frac {1 * 3}{3 * 5} = \frac {1}{5}$

With $\frac {1}{5}$ , we can cross-multiply again with $\frac {5}{7}$ ...

$\frac {1}{5} * \frac {5}{7} = \frac {1 * 5}{5 * 7} = \frac {1}{7}$

Do you see a pattern?

$\frac {1}{7} * \frac {7}{9} = \frac {1 * 7}{7 * 9} = \frac {1}{9}$

The numerator is always 1, while the denominator will be the denominator of the last fraction we just cross-multiplied.

$\frac {1}{9} * \frac {9}{11} = \frac {1 * 9}{9 * 11} = \frac{1}{11}$

Therefore, with the last fraction as $\frac {47}{49}$ , multiplying everything manually will get you $\frac {1}{49}$ , don't you think?

$\frac {1}{47} * \frac {47}{49} = \frac {1 * 47}{47 * 49} = \frac {1}{49}$

This problem then tells us to make that fraction equal to $\frac {a}{b}$ ...

$\frac {1}{49} = \frac {a}{b}$

$a = 1$

$b = 49$

... then tells us to add them together.

$a + b = 1 + 49 = \boxed{50}$

Done!

Its too easy, i got in 2 sec

Cancel them diagonally 1&49 will be left add them up U lk get 50

Just cancel out every same numerator and denominator until 1/49 is left. Add both numbers and you'll get 50

On the surface these types of questions always seem tricky for many of the "mathematically challenged people" (many of whom I don't suppose are reading this right now). What I would honestly say to you is simply to identify a pattern. I have seen many intelligent people try to overthink a problem like this one and get it completely wrong; I see this happening a lot. You must realize that these problems aren't trying to trick you. So the next time you look at one of these questions try not to misatribute what the question is really trying to ask. Hope this comment helps in some way to the people who didn't get the right answer.

Wooooooow easy one was that ..just a simple logic..the 1 St term numerator and the last trems denomentaor does not get cancelled their by u get the a/B fraction sub their value in a+B=1+49=50

I got in 0.1sec 1/49 .1+49=50

By inspection, you can derive 1/49 = a/b, so a+b=50.

Notice the pattern that it cancels out diagonally upward, so it leaves out 1/49. When added together, it becomes 50.

a+b=1+49=50

ALL NOS WILL cut out just 49 will be in the denominator hence 49+1=50