6/9 added to 41/3 in Fraction Form

The result of 6/9 added to 41/3 is: 14 1/3

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions \(\frac69\) and \(\frac413\).

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 9 and 3 is 9.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac69\) to \(\frac{6}9\)
Convert \(\frac413\) to \(\frac{123}9\)

Step 4: Add the Numerators

Add the numerators: 6 + 123 = 129

Step 5: Simplify the Fraction

We can simplify \(\frac1299\) to its lowest form.
The greatest common divisor (GCD) of 129 and 9 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac433\).

Step 6: Convert to Mixed Number

The fraction \(\frac433\) can be written as the mixed number \(14\frac13\).

Final Answer

The result of 6/9 added to 41/3 is:

\[ \frac{6}{9} + \frac{41}{3} = 14\frac13 \]

Understanding Fraction Addition

How to Add Fractions

To add fractions, you need to ensure they have a common denominator. Then add the numerators:

\( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \) (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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