31/194 added to 72/2 in Fraction Form

The result of 31/194 added to 72/2 is: 36 31/194

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions \(\frac31194\) and \(\frac722\).

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 194 and 2 is 194.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac31194\) to \(\frac{31}194\)
Convert \(\frac722\) to \(\frac{6984}194\)

Step 4: Add the Numerators

Add the numerators: 31 + 6984 = 7015

Step 5: Convert to Mixed Number

The fraction \(\frac7015194\) can be written as the mixed number \(36\frac31194\).

Final Answer

The result of 31/194 added to 72/2 is:

\[ \frac{31}{194} + \frac{72}{2} = 36\frac31194 \]

Understanding Fraction Addition

How to Add Fractions

To add fractions, you need to ensure they have a common denominator. Then add the numerators:

\( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \) (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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