83/109 added to 21/6 in Fraction Form

The result of 83/109 added to 21/6 is: 4 57/218

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 109$ and $\frac{2}{1} 6$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 109 and 6 is 654.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 109$ to $\frac{498}{6} 54$
Convert $\frac{2}{1} 6$ to $\frac{2289}{6} 54$

Step 4: Add the Numerators

Add the numerators: 498 + 2289 = 2787

Step 5: Simplify the Fraction

We can simplify $\frac{2}{7} 87654$ to its lowest form.
The greatest common divisor (GCD) of 2787 and 654 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{9}{2} 9218$ .

Step 6: Convert to Mixed Number

The fraction $\frac{9}{2} 9218$ can be written as the mixed number $4 \frac{5}{7} 218$ .

Final Answer

The result of 83/109 added to 21/6 is:

\frac{83}{109} + \frac{21}{6} = 4 \frac{5}{7} 218

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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