31/40 added to 81/3 in Fraction Form

The result of 31/40 added to 81/3 is: 27 31/40

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 40$ and $\frac{8}{1} 3$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 40 and 3 is 120.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 40$ to $\frac{93}{1} 20$
Convert $\frac{8}{1} 3$ to $\frac{3240}{1} 20$

Step 4: Add the Numerators

Add the numerators: 93 + 3240 = 3333

Step 5: Simplify the Fraction

We can simplify $\frac{3}{3} 33120$ to its lowest form.
The greatest common divisor (GCD) of 3333 and 120 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{1} 1140$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{1} 1140$ can be written as the mixed number $27 \frac{3}{1} 40$ .

Final Answer

The result of 31/40 added to 81/3 is:

\frac{31}{40} + \frac{81}{3} = 27 \frac{3}{1} 40

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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