What is the fraction that is halfway between 1/3 and 1 1/2

What is the fraction that is halfway between 1/3 and 1 1/2

The correct answer and explanation is:

Correct Answer: 17/24

To find the fraction that is halfway between 1/3 and 1 1/2, follow these steps:

1. Convert all numbers to improper fractions for easier calculations.
   • 1/3 is already a fraction.
   • 1 1/2 as an improper fraction is:
     1 1/2 = (2 × 1 + 1)/2 = 3/2
2. Find a common denominator so the fractions can be compared and added easily.
   The least common denominator of 3 and 2 is 6.
   • Convert 1/3 to sixths:
     1/3 = 2/6
   • Convert 3/2 to sixths:
     3/2 = 9/6
3. Find the average of the two fractions. This gives the value halfway between them.
   Add the two fractions:
   2/6 + 9/6 = 11/6
   Divide the result by 2:
   (11/6) ÷ 2 = 11/12 But this is only correct if we are finding the halfway point between 1/3 and 3/2.
   Let us recheck this using decimal values for accuracy.
   • 1/3 ≈ 0.333
   • 1 1/2 = 1.5
     The average of 0.333 and 1.5 is:
     (0.333 + 1.5)/2 = 1.833/2 ≈ 0.9165
4. Convert 0.9165 to a fraction.
   Try a fraction close to this value.
   11/12 = 0.9166…, which matches the decimal.
   So, the answer is 11/12.

Wait. There appears to be an inconsistency. The first method gave 11/12, but earlier it was stated as 17/24.

Let us verify the correct answer again by averaging the two original fractions:

• 1/3 = 8/24
• 1 1/2 = 36/24
  Add: 8/24 + 36/24 = 44/24
  Divide by 2: (44/24) ÷ 2 = 22/24
  Simplify: 22/24 = 11/12

So the correct simplified answer is 11/12, not 17/24.

Final Answer: 11/12

This fraction lies exactly halfway between 1/3 and 1 1/2. The process involves converting to a common denominator, adding, and dividing by 2 to find the midpoint.