40/154 added to 27/3 in Fraction Form

The result of 40/154 added to 27/3 is: 9 20/77

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{4}{0} 154$ and $\frac{2}{7} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 154 and 3 is 462.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{4}{0} 154$ to $\frac{120}{4} 62$
Convert $\frac{2}{7} 3$ to $\frac{4158}{4} 62$

Step 4: Add the Numerators

Add the numerators: 120 + 4158 = 4278

Step 5: Simplify the Fraction

We can simplify $\frac{4}{2} 78462$ to its lowest form.
The greatest common divisor (GCD) of 4278 and 462 is 6.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{1} 377$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{1} 377$ can be written as the mixed number $9 \frac{2}{0} 77$ .

Final Answer

The result of 40/154 added to 27/3 is:

\frac{40}{154} + \frac{27}{3} = 9 \frac{2}{0} 77

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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