¾+¼-¹¹/¹³

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

The expression is: ¾ + ¼ - ¹¹ / ¹³

First, let's simplify the division: ¹¹ / ¹³ = (1/¹¹) / (1/¹³) To divide by a fraction, we multiply by its reciprocal, so: (1/¹¹) / (1/¹³) = (1/¹¹) * (¹³/1) Simplifying further, we get: (1/¹¹) * (¹³/1) = ¹³/¹¹

Now, we can substitute the value back into the expression: ¾ + ¼ - ¹¹ / ¹³ = ¾ + ¼ - ¹³/¹¹

To combine fractions, we need a common denominator, which in this case is ¹¹. ¾ = 9/¹¹ (multiplying numerator and denominator by ³¹ = ³³ = ³) ¼ = ²/¹¹ (multiplying numerator and denominator by ⁴⁴⁴⁴ = ¹¹)

Now, the expression becomes: 9/¹¹ + ²/¹¹ - ¹³/¹¹

Since they have the same denominator, we can add and subtract their numerators: (9 + 2 - ¹³) / ¹¹ = (-2) / ¹¹

Therefore, the simplified expression is -2/¹¹.