4,5÷6¾×2⅖

To solve this expression, we will follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).

Let's break down the expression step by step:

4,5 ÷ 6¾ × 2⅖

Step 1: Simplify the fraction 6¾.

To simplify, we convert the mixed number 6¾ to an improper fraction:

6¾ = 6 + ¾ = 6 + 3/4 = 24/4 + 3/4 = 27/4

Now the expression becomes:

4,5 ÷ 27/4 × 2⅖

Step 2: Simplify the mixed number 2⅖.

To simplify, we convert the mixed number 2⅖ to an improper fraction:

2⅖ = 2 + ⅖ = 2 + 2/5 = 10/5 + 2/5 = 12/5

Now the expression becomes:

4,5 ÷ 27/4 × 12/5

Step 3: Perform the division.

To divide, we multiply by the reciprocal of the divisor. The reciprocal of 27/4 is 4/27.

4,5 ÷ 27/4 × 12/5 = 4,5 × 4/27 × 12/5

Step 4: Simplify the expression.

Multiply the numerators and denominators:

4,5 × 4/27 × 12/5 = (4,5 × 4 × 12) / (27 × 5)

= (18 × 4 × 12) / (27 × 5)

Step 5: Simplify the numerator and denominator.

18 × 4 × 12 = 864

27 × 5 = 135

So, the expression simplifies to:

864/135