14/254 added to 19/3 in Fraction Form

The result of 14/254 added to 19/3 is: 6 148/381

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{4} 254$ and $\frac{1}{9} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 254 and 3 is 762.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{4} 254$ to $\frac{42}{7} 62$
Convert $\frac{1}{9} 3$ to $\frac{4826}{7} 62$

Step 4: Add the Numerators

Add the numerators: 42 + 4826 = 4868

Step 5: Simplify the Fraction

We can simplify $\frac{4}{8} 68762$ to its lowest form.
The greatest common divisor (GCD) of 4868 and 762 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{4} 34381$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{4} 34381$ can be written as the mixed number $6 \frac{1}{4} 8381$ .

Final Answer

The result of 14/254 added to 19/3 is:

\frac{14}{254} + \frac{19}{3} = 6 \frac{1}{4} 8381

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).

Fraction Calculator

Calculate operations between any two fractions: