77/82 added to 83/2 in Fraction Form

The result of 77/82 added to 83/2 is: 42 18/41

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{7}{7} 82$ and $\frac{8}{3} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 82 and 2 is 82.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{7}{7} 82$ to $\frac{77}{8} 2$
Convert $\frac{8}{3} 2$ to $\frac{3403}{8} 2$

Step 4: Add the Numerators

Add the numerators: 77 + 3403 = 3480

Step 5: Simplify the Fraction

We can simplify $\frac{3}{4} 8082$ to its lowest form.
The greatest common divisor (GCD) of 3480 and 82 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{7} 4041$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{7} 4041$ can be written as the mixed number $42 \frac{1}{8} 41$ .

Final Answer

The result of 77/82 added to 83/2 is:

\frac{77}{82} + \frac{83}{2} = 42 \frac{1}{8} 41

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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