171/15 added to 101/4 in Fraction Form

The result of 171/15 added to 101/4 is: 36 13/20

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{7} 115$ and $\frac{1}{0} 14$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 15 and 4 is 60.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{7} 115$ to $\frac{684}{6} 0$
Convert $\frac{1}{0} 14$ to $\frac{1515}{6} 0$

Step 4: Add the Numerators

Add the numerators: 684 + 1515 = 2199

Step 5: Simplify the Fraction

We can simplify $\frac{2}{1} 9960$ to its lowest form.
The greatest common divisor (GCD) of 2199 and 60 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{3} 320$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{3} 320$ can be written as the mixed number $36 \frac{1}{3} 20$ .

Final Answer

The result of 171/15 added to 101/4 is:

\frac{171}{15} + \frac{101}{4} = 36 \frac{1}{3} 20

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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