31/71 added to 74/4 in Fraction Form

The result of 31/71 added to 74/4 is: 18 133/142

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 71$ and $\frac{7}{4} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 71 and 4 is 284.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 71$ to $\frac{124}{2} 84$
Convert $\frac{7}{4} 4$ to $\frac{5254}{2} 84$

Step 4: Add the Numerators

Add the numerators: 124 + 5254 = 5378

Step 5: Simplify the Fraction

We can simplify $\frac{5}{3} 78284$ to its lowest form.
The greatest common divisor (GCD) of 5378 and 284 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{6} 89142$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{6} 89142$ can be written as the mixed number $18 \frac{1}{3} 3142$ .

Final Answer

The result of 31/71 added to 74/4 is:

\frac{31}{71} + \frac{74}{4} = 18 \frac{1}{3} 3142

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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