135/40 added to 82/3 in Fraction Form

The result of 135/40 added to 82/3 is: 30 17/24

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{3} 540$ and $\frac{8}{2} 3$ .

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 $\frac{1}{3} 540$ to $\frac{405}{1} 20$
Convert $\frac{8}{2} 3$ to $\frac{3280}{1} 20$

Step 4: Add the Numerators

Add the numerators: 405 + 3280 = 3685

Step 5: Simplify the Fraction

We can simplify $\frac{3}{6} 85120$ to its lowest form.
The greatest common divisor (GCD) of 3685 and 120 is 5.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{3} 724$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{3} 724$ can be written as the mixed number $30 \frac{1}{7} 24$ .

Final Answer

The result of 135/40 added to 82/3 is:

\frac{135}{40} + \frac{82}{3} = 30 \frac{1}{7} 24

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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