83/213 added to 34/4 in Fraction Form

The result of 83/213 added to 34/4 is: 8 379/426

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 213$ and $\frac{3}{4} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 213 and 4 is 852.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 213$ to $\frac{332}{8} 52$
Convert $\frac{3}{4} 4$ to $\frac{7242}{8} 52$

Step 4: Add the Numerators

Add the numerators: 332 + 7242 = 7574

Step 5: Simplify the Fraction

We can simplify $\frac{7}{5} 74852$ to its lowest form.
The greatest common divisor (GCD) of 7574 and 852 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{3}{7} 87426$ .

Step 6: Convert to Mixed Number

The fraction $\frac{3}{7} 87426$ can be written as the mixed number $8 \frac{3}{7} 9426$ .

Final Answer

The result of 83/213 added to 34/4 is:

\frac{83}{213} + \frac{34}{4} = 8 \frac{3}{7} 9426

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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