19/38 added to 74/3 in Fraction Form

The result of 19/38 added to 74/3 is: 25 1/6

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{9} 38$ and $\frac{7}{4} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 38 and 3 is 114.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{9} 38$ to $\frac{57}{1} 14$
Convert $\frac{7}{4} 3$ to $\frac{2812}{1} 14$

Step 4: Add the Numerators

Add the numerators: 57 + 2812 = 2869

Step 5: Simplify the Fraction

We can simplify $\frac{2}{8} 69114$ to its lowest form.
The greatest common divisor (GCD) of 2869 and 114 is 19.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{5} 16$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{5} 16$ can be written as the mixed number $25 \frac{1}{6}$ .

Final Answer

The result of 19/38 added to 74/3 is:

\frac{19}{38} + \frac{74}{3} = 25 \frac{1}{6}

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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