31/118 added to 83/2 in Fraction Form

The result of 31/118 added to 83/2 is: 41 45/59

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 118$ and $\frac{8}{3} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 118 and 2 is 118.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 118$ to $\frac{31}{1} 18$
Convert $\frac{8}{3} 2$ to $\frac{4897}{1} 18$

Step 4: Add the Numerators

Add the numerators: 31 + 4897 = 4928

Step 5: Simplify the Fraction

We can simplify $\frac{4}{9} 28118$ to its lowest form.
The greatest common divisor (GCD) of 4928 and 118 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{4} 6459$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{4} 6459$ can be written as the mixed number $41 \frac{4}{5} 59$ .

Final Answer

The result of 31/118 added to 83/2 is:

\frac{31}{118} + \frac{83}{2} = 41 \frac{4}{5} 59

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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