27/21 added to 23/8 in Fraction Form

The result of 27/21 added to 23/8 is: 4 9/56

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{2}{7} 21$ and $\frac{2}{3} 8$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 21 and 8 is 168.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{2}{7} 21$ to $\frac{216}{1} 68$
Convert $\frac{2}{3} 8$ to $\frac{483}{1} 68$

Step 4: Add the Numerators

Add the numerators: 216 + 483 = 699

Step 5: Simplify the Fraction

We can simplify $\frac{6}{9} 9168$ to its lowest form.
The greatest common divisor (GCD) of 699 and 168 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{3} 356$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{3} 356$ can be written as the mixed number $4 \frac{9}{5} 6$ .

Final Answer

The result of 27/21 added to 23/8 is:

\frac{27}{21} + \frac{23}{8} = 4 \frac{9}{5} 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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