My improper fraction is equivalent to 4 4/9.
The numerator is between 110 and 170.
The denominator is between 30 and 50.
What improper fraction is Mason thinking of?
Let's first write 4 4/9 as an improper fraction:
4 4/9 = 40/9
To find the actual fraction Mason is thinking of, we need to find a numerator and denominator that are equivalent to 40/9 and also satisfy the given ranges.
Let's start by finding the possible denominators: between 30 and 50, the only denominator that is a factor of 9 is 36. So we can start by setting the denominator as 36:
40/9 = (40*4)/(9*4) = 160/36
Now we need to check if the numerator 160 is between 110 and 170:
110 ≤ 160 ≤ 170
This is true, so we have found the fraction:
160/36
This fraction is equivalent to 4 4/9 and satisfies the given ranges for the numerator and denominator. Therefore, Mason is thinking of the fraction 160/36.