180/101 added to 21/3 in Fraction Form

The result of 180/101 added to 21/3 is: 8 79/101

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions 180101 and 213.

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 101 and 3 is 303.

Step 3: Convert Fractions to Equivalent Fractions

Convert 180101 to 540303
Convert 213 to 2121303

Step 4: Add the Numerators

Add the numerators: 540 + 2121 = 2661

Step 5: Simplify the Fraction

We can simplify 2661303 to its lowest form.
The greatest common divisor (GCD) of 2661 and 303 is 3.
Dividing both numerator and denominator by the GCD, we get 887101.

Step 6: Convert to Mixed Number

The fraction 887101 can be written as the mixed number 879101.

Final Answer

The result of 180/101 added to 21/3 is:

180101+213=879101

Understanding Fraction Addition

How to Add Fractions

To add fractions, you need to ensure they have a common denominator. Then add the numerators:

ab+cd=ad+bcbd (when denominators are different)

Or simply ab+cb=a+cb (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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