117/27 added to 83/2 in Fraction Form

The result of 117/27 added to 83/2 is: 45 5/6

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{1} 727$ and $\frac{8}{3} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 27 and 2 is 54.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{1} 727$ to $\frac{234}{5} 4$
Convert $\frac{8}{3} 2$ to $\frac{2241}{5} 4$

Step 4: Add the Numerators

Add the numerators: 234 + 2241 = 2475

Step 5: Simplify the Fraction

We can simplify $\frac{2}{4} 7554$ to its lowest form.
The greatest common divisor (GCD) of 2475 and 54 is 9.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{7} 56$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{7} 56$ can be written as the mixed number $45 \frac{5}{6}$ .

Final Answer

The result of 117/27 added to 83/2 is:

\frac{117}{27} + \frac{83}{2} = 45 \frac{5}{6}

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: