83/67 added to 142/2 in Fraction Form

The result of 83/67 added to 142/2 is: 72 16/67

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 67$ and $\frac{1}{4} 22$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 67 and 2 is 134.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 67$ to $\frac{166}{1} 34$
Convert $\frac{1}{4} 22$ to $\frac{9514}{1} 34$

Step 4: Add the Numerators

Add the numerators: 166 + 9514 = 9680

Step 5: Simplify the Fraction

We can simplify $\frac{9}{6} 80134$ to its lowest form.
The greatest common divisor (GCD) of 9680 and 134 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{4}{8} 4067$ .

Step 6: Convert to Mixed Number

The fraction $\frac{4}{8} 4067$ can be written as the mixed number $72 \frac{1}{6} 67$ .

Final Answer

The result of 83/67 added to 142/2 is:

\frac{83}{67} + \frac{142}{2} = 72 \frac{1}{6} 67

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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