77/108 added to 127/4 in Fraction Form

The result of 77/108 added to 127/4 is: 32 25/54

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{7}{7} 108$ and $\frac{1}{2} 74$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 108 and 4 is 108.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{7}{7} 108$ to $\frac{77}{1} 08$
Convert $\frac{1}{2} 74$ to $\frac{3429}{1} 08$

Step 4: Add the Numerators

Add the numerators: 77 + 3429 = 3506

Step 5: Simplify the Fraction

We can simplify $\frac{3}{5} 06108$ to its lowest form.
The greatest common divisor (GCD) of 3506 and 108 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{7} 5354$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{7} 5354$ can be written as the mixed number $32 \frac{2}{5} 54$ .

Final Answer

The result of 77/108 added to 127/4 is:

\frac{77}{108} + \frac{127}{4} = 32 \frac{2}{5} 54

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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