83/85 added to 141/4 in Fraction Form

The result of 83/85 added to 141/4 is: 36 77/340

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 85$ and $\frac{1}{4} 14$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 85 and 4 is 340.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 85$ to $\frac{332}{3} 40$
Convert $\frac{1}{4} 14$ to $\frac{11985}{3} 40$

Step 4: Add the Numerators

Add the numerators: 332 + 11985 = 12317

Step 5: Convert to Mixed Number

The fraction $\frac{1}{2} 317340$ can be written as the mixed number $36 \frac{7}{7} 340$ .

Final Answer

The result of 83/85 added to 141/4 is:

\frac{83}{85} + \frac{141}{4} = 36 \frac{7}{7} 340

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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