Short Answer 
The process involves converting the mixed number 2 8 5 into the improper fraction 8/21, setting up a proportion with a new denominator of 16x, and solving for x, resulting in x = 42. Ultimately, the equivalent fraction is 16/42, which simplifies back to 8/21.
Step 1: Convert to Improper Fraction
To find the equivalent fraction for 2 8 5, start by converting it into an improper fraction. This is done using the formula:
- Improper Fraction = Whole Number √ó Denominator + Numerator
- For 2 8 5: 2 √ó 8 + 5 = 16 + 5 = 21
- So, 2 8 5 = 8/21
Step 2: Set Up the Proportion
Next, establish a proportion using the improper fraction you found and the new denominator 16x. Set it up as:
- 8/21 = 16/x
- This proportional relationship allows you to find the value of x.
Step 3: Solve for x
To determine the value of x, cross-multiply the terms in the proportion:
- 21 √ó 16 = 8 √ó x
- This simplifies to: 336 = 8x
- Next, divide both sides by 8 to solve for x: x = 336/8 = 42
Thus, the equivalent fraction is 16/42, which can also be simplified to 8/21.