My improper fraction is equivalent to 4 4/9.

Question

The numerator is between 110 and 170.
The denominator is between 30 and 50.
What improper fraction is Mason thinking of?

Answer 1

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.