135/85 added to 34/3 in Fraction Form

The result of 135/85 added to 34/3 is: 12 47/51

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{3} 585$ and $\frac{3}{4} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 85 and 3 is 255.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{3} 585$ to $\frac{405}{2} 55$
Convert $\frac{3}{4} 3$ to $\frac{2890}{2} 55$

Step 4: Add the Numerators

Add the numerators: 405 + 2890 = 3295

Step 5: Simplify the Fraction

We can simplify $\frac{3}{2} 95255$ to its lowest form.
The greatest common divisor (GCD) of 3295 and 255 is 5.
Dividing both numerator and denominator by the GCD, we get $\frac{6}{5} 951$ .

Step 6: Convert to Mixed Number

The fraction $\frac{6}{5} 951$ can be written as the mixed number $12 \frac{4}{7} 51$ .

Final Answer

The result of 135/85 added to 34/3 is:

\frac{135}{85} + \frac{34}{3} = 12 \frac{4}{7} 51

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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