83/19 added to 21/3 in Fraction Form

The result of 83/19 added to 21/3 is: 11 7/19

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 19$ and $\frac{2}{1} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 19 and 3 is 57.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 19$ to $\frac{249}{5} 7$
Convert $\frac{2}{1} 3$ to $\frac{399}{5} 7$

Step 4: Add the Numerators

Add the numerators: 249 + 399 = 648

Step 5: Simplify the Fraction

We can simplify $\frac{6}{4} 857$ to its lowest form.
The greatest common divisor (GCD) of 648 and 57 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{1} 619$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{1} 619$ can be written as the mixed number $11 \frac{7}{1} 9$ .

Final Answer

The result of 83/19 added to 21/3 is:

\frac{83}{19} + \frac{21}{3} = 11 \frac{7}{1} 9

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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