67/109 added to 158/4 in Fraction Form

The result of 67/109 added to 158/4 is: 40 25/218

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{6}{7} 109$ and $\frac{1}{5} 84$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 109 and 4 is 436.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{6}{7} 109$ to $\frac{268}{4} 36$
Convert $\frac{1}{5} 84$ to $\frac{17222}{4} 36$

Step 4: Add the Numerators

Add the numerators: 268 + 17222 = 17490

Step 5: Simplify the Fraction

We can simplify $\frac{1}{7} 490436$ to its lowest form.
The greatest common divisor (GCD) of 17490 and 436 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{8}{7} 45218$ .

Step 6: Convert to Mixed Number

The fraction $\frac{8}{7} 45218$ can be written as the mixed number $40 \frac{2}{5} 218$ .

Final Answer

The result of 67/109 added to 158/4 is:

\frac{67}{109} + \frac{158}{4} = 40 \frac{2}{5} 218

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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