31/86 added to 101/6 in Fraction Form

The result of 31/86 added to 101/6 is: 17 25/129

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 86$ and $\frac{1}{0} 16$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 86 and 6 is 258.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 86$ to $\frac{93}{2} 58$
Convert $\frac{1}{0} 16$ to $\frac{4343}{2} 58$

Step 4: Add the Numerators

Add the numerators: 93 + 4343 = 4436

Step 5: Simplify the Fraction

We can simplify $\frac{4}{4} 36258$ to its lowest form.
The greatest common divisor (GCD) of 4436 and 258 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{2} 18129$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{2} 18129$ can be written as the mixed number $17 \frac{2}{5} 129$ .

Final Answer

The result of 31/86 added to 101/6 is:

\frac{31}{86} + \frac{101}{6} = 17 \frac{2}{5} 129

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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