21/114 added to 154/2 in Fraction Form

The result of 21/114 added to 154/2 is: 77 7/38

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{2}{1} 114$ and $\frac{1}{5} 42$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 114 and 2 is 114.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{2}{1} 114$ to $\frac{21}{1} 14$
Convert $\frac{1}{5} 42$ to $\frac{8778}{1} 14$

Step 4: Add the Numerators

Add the numerators: 21 + 8778 = 8799

Step 5: Simplify the Fraction

We can simplify $\frac{8}{7} 99114$ to its lowest form.
The greatest common divisor (GCD) of 8799 and 114 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{9} 3338$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{9} 3338$ can be written as the mixed number $77 \frac{7}{3} 8$ .

Final Answer

The result of 21/114 added to 154/2 is:

\frac{21}{114} + \frac{154}{2} = 77 \frac{7}{3} 8

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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