42/81 added to 83/3 in Fraction Form

The result of 42/81 added to 83/3 is: 28 5/27

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{4}{2} 81$ and $\frac{8}{3} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 81 and 3 is 81.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{4}{2} 81$ to $\frac{42}{8} 1$
Convert $\frac{8}{3} 3$ to $\frac{2241}{8} 1$

Step 4: Add the Numerators

Add the numerators: 42 + 2241 = 2283

Step 5: Simplify the Fraction

We can simplify $\frac{2}{2} 8381$ to its lowest form.
The greatest common divisor (GCD) of 2283 and 81 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{6} 127$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{6} 127$ can be written as the mixed number $28 \frac{5}{2} 7$ .

Final Answer

The result of 42/81 added to 83/3 is:

\frac{42}{81} + \frac{83}{3} = 28 \frac{5}{2} 7

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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