4,5:6¾×2⅖

To solve this expression, we can follow the order of operations (PEMDAS):

1. Start by finding the product of 6¾ and 2⅖:

   6¾ × 2⅖

   Convert both mixed numbers to improper fractions:

   6¾ = (4 * 3 + 3)/4 = 27/4 2⅖ = (2 * 5 + 2)/5 = 12/5

   Multiply the fractions:

   (27/4) × (12/5)

   Multiply the numerators to get the new numerator:

   27 × 12 = 324

   Multiply the denominators to get the new denominator:

   4 × 5 = 20

   Simplify the fraction if possible:

   324/20 = 27/5

2. Now we have:

   4,5: (27/5)

   To divide by a fraction, we can multiply by its reciprocal:

   4,5 × (5/27)

   Multiply the numerators:

   4,5 × 5 = 22,5

   Multiply the denominators:

   27

   Simplify the fraction if possible:

   22,5/27 is already in its simplest form.

Therefore, the expression 4,5:6¾×2⅖ simplifies to 22,5/27.