83/32 added to 192/3 in Fraction Form

The result of 83/32 added to 192/3 is: 66 19/32

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 32$ and $\frac{1}{9} 23$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 32 and 3 is 96.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 32$ to $\frac{249}{9} 6$
Convert $\frac{1}{9} 23$ to $\frac{6144}{9} 6$

Step 4: Add the Numerators

Add the numerators: 249 + 6144 = 6393

Step 5: Simplify the Fraction

We can simplify $\frac{6}{3} 9396$ to its lowest form.
The greatest common divisor (GCD) of 6393 and 96 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{1} 3132$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{1} 3132$ can be written as the mixed number $66 \frac{1}{9} 32$ .

Final Answer

The result of 83/32 added to 192/3 is:

\frac{83}{32} + \frac{192}{3} = 66 \frac{1}{9} 32

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: