27/31 added to 213/3 in Fraction Form

The result of 27/31 added to 213/3 is: 71 27/31

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{2}{7} 31$ and $\frac{2}{1} 33$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 31 and 3 is 93.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{2}{7} 31$ to $\frac{81}{9} 3$
Convert $\frac{2}{1} 33$ to $\frac{6603}{9} 3$

Step 4: Add the Numerators

Add the numerators: 81 + 6603 = 6684

Step 5: Simplify the Fraction

We can simplify $\frac{6}{6} 8493$ to its lowest form.
The greatest common divisor (GCD) of 6684 and 93 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{2} 2831$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{2} 2831$ can be written as the mixed number $71 \frac{2}{7} 31$ .

Final Answer

The result of 27/31 added to 213/3 is:

\frac{27}{31} + \frac{213}{3} = 71 \frac{2}{7} 31

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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