I am a fraction whose numerator and denominator are both prime numbers less than 20. if you were to increase each term by 1, I would be equivalent to 1/2. what fraction am I?
I got 3/7. If you increase the numerator and the denominator by 1 it equals 4/8 or 1/2. There are multiple awnsers.
Just try different combinations of prime numbers over each other. I got three sevenths.
To solve this problem, let's follow the given information step by step.
First, identify the fraction whose numerator and denominator are both prime numbers less than 20. The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, and 19. We need to find a fraction using these numbers as both numerator and denominator.
Next, assume the fraction as x/y, where x is the numerator and y is the denominator.
Now, according to the given information, if we increase each term by 1, the fraction becomes (x + 1)/(y + 1). We are told that this new fraction is equivalent to 1/2.
Using this information, we can set up the equation: (x + 1)/(y + 1) = 1/2.
To solve this equation, we can cross-multiply: 2(x + 1) = y + 1.
Expanding the left side of the equation, we have: 2x + 2 = y + 1.
Rearranging the equation, we get: 2x - y = -1.
Now, we need to find the values of x and y that satisfy this equation and also have both x and y as prime numbers less than 20.
We can start by trying different values for x and y, using the prime numbers less than 20 as options.
By substituting values for x and y and checking if the equation holds true, we can find the correct fraction.
Let's try different values:
- x = 2, y = 3: 2(2) - 3 = -1, so this doesn't work.
- x = 2, y = 5: 2(2) - 5 = -1, so this doesn't work.
- x = 2, y = 7: 2(2) - 7 = -3, so this doesn't work.
- x = 2, y = 11: 2(2) - 11 = -7, so this doesn't work.
- x = 2, y = 13: 2(2) - 13 = -9, so this doesn't work.
- x = 2, y = 17: 2(2) - 17 = -13, so this doesn't work.
- x = 2, y = 19: 2(2) - 19 = -15, so this doesn't work.
- x = 3, y = 2: 2(3) - 2 = 4, so this doesn't work.
- x = 3, y = 5: 2(3) - 5 = 1, so this works! The fraction is 3/5.
Therefore, the fraction you are referring to is 3/5.
There are quite a few answers to this.
First, the prime numbers below 20 are 2,3,5,7,11,13,17,19
So, you've got 2/5 and 3/7 and 5/11 and 9/19. Add one to the numerator and denominator of each and you get 3/6, 4/8, 6/12 and 10/20.
Not sure which one they wanted.