83/199 added to 2/2 in Fraction Form

The result of 83/199 added to 2/2 is: 1 83/199

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 199$ and $\frac{2}{2}$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 199 and 2 is 398.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 199$ to $\frac{166}{3} 98$
Convert $\frac{2}{2}$ to $\frac{398}{3} 98$

Step 4: Add the Numerators

Add the numerators: 166 + 398 = 564

Step 5: Simplify the Fraction

We can simplify $\frac{5}{6} 4398$ to its lowest form.
The greatest common divisor (GCD) of 564 and 398 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{8} 2199$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{8} 2199$ can be written as the mixed number $1 \frac{8}{3} 199$ .

Final Answer

The result of 83/199 added to 2/2 is:

\frac{83}{199} + \frac{2}{2} = 1 \frac{8}{3} 199

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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