135/42 added to 67/2 in Fraction Form

The result of 135/42 added to 67/2 is: 36 5/7

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{3} 542$ and $\frac{6}{7} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 42 and 2 is 42.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{3} 542$ to $\frac{135}{4} 2$
Convert $\frac{6}{7} 2$ to $\frac{1407}{4} 2$

Step 4: Add the Numerators

Add the numerators: 135 + 1407 = 1542

Step 5: Simplify the Fraction

We can simplify $\frac{1}{5} 4242$ to its lowest form.
The greatest common divisor (GCD) of 1542 and 42 is 6.
Dividing both numerator and denominator by the GCD, we get $\frac{2}{5} 77$ .

Step 6: Convert to Mixed Number

The fraction $\frac{2}{5} 77$ can be written as the mixed number $36 \frac{5}{7}$ .

Final Answer

The result of 135/42 added to 67/2 is:

\frac{135}{42} + \frac{67}{2} = 36 \frac{5}{7}

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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