I am a fraction between 1/3 and 1/5 My dominator is 1 less than 4 times my numerator. What fraction am I?
I am the smallest fraction between 2/3 and 3/4. My numerator is 7 less than my dominator. What fraction am I?
D=4n-1
(1/3)less than (n/d) less than (1/5)
(1/3) less than(n/(4n-1)) less than (1/5)
Solve the between statement
To solve this problem, let's break it down step by step.
First, let's determine the value of the numerator. We are given that the fraction is between 1/3 and 1/5, so the numerator must be greater than 1/5 and less than 1/3. To find a common denominator, we can multiply 1/5 by 3/3 and multiply 1/3 by 5/5:
1/5 * 3/3 = 3/15
1/3 * 5/5 = 5/15
Therefore, the numerator must be greater than 3/15 and less than 5/15.
Next, let's determine the denominator. We are told that the denominator is 1 less than 4 times the numerator. So, we can set up an equation:
Denominator = 4 * Numerator - 1
Substituting the possible values for the numerator that we found earlier:
Denominator = 4 * (3/15) - 1 = 12/15 - 1 = 12/15 - 15/15 = -3/15
Denominator = 4 * (5/15) - 1 = 20/15 - 1 = 20/15 - 15/15 = 5/15
Now, let's put the numerator and denominator together to form the fraction:
Numerator = 3/15 (The numerator is greater than 3/15 and less than 5/15)
Denominator = 5/15
So the fraction is 3/15, which can be simplified to 1/5.
Therefore, you are the fraction 1/5.