78/127 added to 138/4 in Fraction Form

The result of 78/127 added to 138/4 is: 35 29/254

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{7}{8} 127$ and $\frac{1}{3} 84$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 127 and 4 is 508.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{7}{8} 127$ to $\frac{312}{5} 08$
Convert $\frac{1}{3} 84$ to $\frac{17526}{5} 08$

Step 4: Add the Numerators

Add the numerators: 312 + 17526 = 17838

Step 5: Simplify the Fraction

We can simplify $\frac{1}{7} 838508$ to its lowest form.
The greatest common divisor (GCD) of 17838 and 508 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{8}{9} 19254$ .

Step 6: Convert to Mixed Number

The fraction $\frac{8}{9} 19254$ can be written as the mixed number $35 \frac{2}{9} 254$ .

Final Answer

The result of 78/127 added to 138/4 is:

\frac{78}{127} + \frac{138}{4} = 35 \frac{2}{9} 254

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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