Problem

Evaluate. \[ \left(\frac{2}{3}+\frac{1}{4}\right) \div \frac{5}{6} \] Write your answer in simplest form.

Solution

Step 1 :First, we need to add the fractions inside the parentheses. To add fractions, we need to find a common denominator. The least common denominator (LCD) of 3 and 4 is 12. So, we rewrite the fractions with the LCD as the denominator: \(\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\) and \(\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\).

Step 2 :Now, we can add the fractions: \(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\). So, the expression becomes: \(\frac{11}{12} \div \frac{5}{6}\).

Step 3 :To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: \(\frac{11}{12} \times \frac{6}{5} = \frac{11 \times 6}{12 \times 5} = \frac{66}{60}\).

Step 4 :The fraction \(\frac{66}{60}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6: \(\frac{66 \div 6}{60 \div 6} = \frac{11}{10}\).

Step 5 :So, the simplest form of the result is \(\boxed{\frac{11}{10}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/Wj5gNbjJrg/

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