21/77 added to 67/2 in Fraction Form

The result of 21/77 added to 67/2 is: 33 17/22

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{2}{1} 77$ and $\frac{6}{7} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 77 and 2 is 154.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{2}{1} 77$ to $\frac{42}{1} 54$
Convert $\frac{6}{7} 2$ to $\frac{5159}{1} 54$

Step 4: Add the Numerators

Add the numerators: 42 + 5159 = 5201

Step 5: Simplify the Fraction

We can simplify $\frac{5}{2} 01154$ to its lowest form.
The greatest common divisor (GCD) of 5201 and 154 is 7.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{4} 322$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{4} 322$ can be written as the mixed number $33 \frac{1}{7} 22$ .

Final Answer

The result of 21/77 added to 67/2 is:

\frac{21}{77} + \frac{67}{2} = 33 \frac{1}{7} 22

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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