19/83 added to 164/2 in Fraction Form

The result of 19/83 added to 164/2 is: 82 19/83

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{9} 83$ and $\frac{1}{6} 42$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 83 and 2 is 166.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{9} 83$ to $\frac{38}{1} 66$
Convert $\frac{1}{6} 42$ to $\frac{13612}{1} 66$

Step 4: Add the Numerators

Add the numerators: 38 + 13612 = 13650

Step 5: Simplify the Fraction

We can simplify $\frac{1}{3} 650166$ to its lowest form.
The greatest common divisor (GCD) of 13650 and 166 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{6}{8} 2583$ .

Step 6: Convert to Mixed Number

The fraction $\frac{6}{8} 2583$ can be written as the mixed number $82 \frac{1}{9} 83$ .

Final Answer

The result of 19/83 added to 164/2 is:

\frac{19}{83} + \frac{164}{2} = 82 \frac{1}{9} 83

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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