¾+¼-¹¹/¹³

To solve the expression ¾+¼-¹¹/¹³, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, there are no parentheses or exponents, so we move on to multiplication and division.

Next, we have ¹¹/¹³. To divide fractions, you need to multiply the numerator of the first fraction by the denominator of the second fraction and the denominator of the first fraction by the numerator of the second fraction.

Thus, ¹¹/¹³ is equal to (11 * 1) / (1 * 13) = 11/13.

Now we are left with ¾ + ¼ - 11/13.

To add or subtract fractions, the denominators must be the same. In this case, the denominators are different, so we need to find a common denominator. The common denominator here is 12.

Converting ¾ to twelfths, we get 9/12.

Converting ¼ to twelfths, we get 3/12.

Now our expression becomes: 9/12 + 3/12 - 11/13.

Now that the denominators are the same, we can add and subtract numerators:

9/12 + 3/12 - 11/13 = (9 + 3) /12 - 11/13 = 12/12 - 11/13.

12/12 is equal to 1, so now we have:

1 - 11/13.

To subtract fractions, the same denominator is required. We can convert 1 to thirteenths by multiplying the numerator and the denominator by 13:

1 = 13/13.

Now our expression becomes:

13/13 - 11/13 = (13 - 11)/13 = 2/13.

Therefore, the expression ¾ + ¼ - ¹¹/¹³ equals 2/13.