67/71 added to 178/2 in Fraction Form

The result of 67/71 added to 178/2 is: 89 67/71

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{6}{7} 71$ and $\frac{1}{7} 82$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 71 and 2 is 142.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{6}{7} 71$ to $\frac{134}{1} 42$
Convert $\frac{1}{7} 82$ to $\frac{12638}{1} 42$

Step 4: Add the Numerators

Add the numerators: 134 + 12638 = 12772

Step 5: Simplify the Fraction

We can simplify $\frac{1}{2} 772142$ to its lowest form.
The greatest common divisor (GCD) of 12772 and 142 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{6}{3} 8671$ .

Step 6: Convert to Mixed Number

The fraction $\frac{6}{3} 8671$ can be written as the mixed number $89 \frac{6}{7} 71$ .

Final Answer

The result of 67/71 added to 178/2 is:

\frac{67}{71} + \frac{178}{2} = 89 \frac{6}{7} 71

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).

Fraction Calculator

Calculate operations between any two fractions: