31/204 added to 101/4 in Fraction Form

The result of 31/204 added to 101/4 is: 25 41/102

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 204$ and $\frac{1}{0} 14$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 204 and 4 is 204.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 204$ to $\frac{31}{2} 04$
Convert $\frac{1}{0} 14$ to $\frac{5151}{2} 04$

Step 4: Add the Numerators

Add the numerators: 31 + 5151 = 5182

Step 5: Simplify the Fraction

We can simplify $\frac{5}{1} 82204$ to its lowest form.
The greatest common divisor (GCD) of 5182 and 204 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{5} 91102$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{5} 91102$ can be written as the mixed number $25 \frac{4}{1} 102$ .

Final Answer

The result of 31/204 added to 101/4 is:

\frac{31}{204} + \frac{101}{4} = 25 \frac{4}{1} 102

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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