13/208 added to 41/4 in Fraction Form

The result of 13/208 added to 41/4 is: 10 5/16

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{3} 208$ and $\frac{4}{1} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 208 and 4 is 208.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{3} 208$ to $\frac{13}{2} 08$
Convert $\frac{4}{1} 4$ to $\frac{2132}{2} 08$

Step 4: Add the Numerators

Add the numerators: 13 + 2132 = 2145

Step 5: Simplify the Fraction

We can simplify $\frac{2}{1} 45208$ to its lowest form.
The greatest common divisor (GCD) of 2145 and 208 is 13.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{6} 516$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{6} 516$ can be written as the mixed number $10 \frac{5}{1} 6$ .

Final Answer

The result of 13/208 added to 41/4 is:

\frac{13}{208} + \frac{41}{4} = 10 \frac{5}{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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