31/154 added to 103/2 in Fraction Form

The result of 31/154 added to 103/2 is: 51 54/77

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions \(\frac31154\) and \(\frac1032\).

Step 2: Find the Least Common Multiple (LCM)

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

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac31154\) to \(\frac{31}154\)
Convert \(\frac1032\) to \(\frac{7931}154\)

Step 4: Add the Numerators

Add the numerators: 31 + 7931 = 7962

Step 5: Simplify the Fraction

We can simplify \(\frac7962154\) to its lowest form.
The greatest common divisor (GCD) of 7962 and 154 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac398177\).

Step 6: Convert to Mixed Number

The fraction \(\frac398177\) can be written as the mixed number \(51\frac5477\).

Final Answer

The result of 31/154 added to 103/2 is:

\[ \frac{31}{154} + \frac{103}{2} = 51\frac5477 \]

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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