21/243 added to 7/3 in Fraction Form

The result of 21/243 added to 7/3 is: 2 34/81

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{2}{1} 243$ and $\frac{7}{3}$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 243 and 3 is 243.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{2}{1} 243$ to $\frac{21}{2} 43$
Convert $\frac{7}{3}$ to $\frac{567}{2} 43$

Step 4: Add the Numerators

Add the numerators: 21 + 567 = 588

Step 5: Simplify the Fraction

We can simplify $\frac{5}{8} 8243$ to its lowest form.
The greatest common divisor (GCD) of 588 and 243 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{9} 681$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{9} 681$ can be written as the mixed number $2 \frac{3}{4} 81$ .

Final Answer

The result of 21/243 added to 7/3 is:

\frac{21}{243} + \frac{7}{3} = 2 \frac{3}{4} 81

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: