31/127 added to 138/6 in Fraction Form

The result of 31/127 added to 138/6 is: 23 31/127

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 127$ and $\frac{1}{3} 86$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 127 and 6 is 762.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 127$ to $\frac{186}{7} 62$
Convert $\frac{1}{3} 86$ to $\frac{17526}{7} 62$

Step 4: Add the Numerators

Add the numerators: 186 + 17526 = 17712

Step 5: Simplify the Fraction

We can simplify $\frac{1}{7} 712762$ to its lowest form.
The greatest common divisor (GCD) of 17712 and 762 is 6.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{9} 52127$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{9} 52127$ can be written as the mixed number $23 \frac{3}{1} 127$ .

Final Answer

The result of 31/127 added to 138/6 is:

\frac{31}{127} + \frac{138}{6} = 23 \frac{3}{1} 127

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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