65/182 added to 81/2 in Fraction Form

The result of 65/182 added to 81/2 is: 40 6/7

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{6}{5} 182$ and $\frac{8}{1} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 182 and 2 is 182.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{6}{5} 182$ to $\frac{65}{1} 82$
Convert $\frac{8}{1} 2$ to $\frac{7371}{1} 82$

Step 4: Add the Numerators

Add the numerators: 65 + 7371 = 7436

Step 5: Simplify the Fraction

We can simplify $\frac{7}{4} 36182$ to its lowest form.
The greatest common divisor (GCD) of 7436 and 182 is 26.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{8} 67$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{8} 67$ can be written as the mixed number $40 \frac{6}{7}$ .

Final Answer

The result of 65/182 added to 81/2 is:

\frac{65}{182} + \frac{81}{2} = 40 \frac{6}{7}

Understanding Fraction Addition

How to Add Fractions

To add fractions, you need to ensure they have a common denominator. Then add the numerators:

$\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}$ (when denominators are different)

Or simply $\frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}$ (when denominators are the same)

Why Simplify Fractions?

Simplifying fractions makes them easier to work with and understand. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

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