21/107 subtracted by 213/6 in Fraction Form

The result of 21/107 subtracted by 213/6 is: -36 149/214

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2136\) from \(\frac21107\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 107 and 6 is 642.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac21107\) to \(\frac{126}642\)
Convert \(\frac2136\) to \(\frac{22791}642\)

Step 4: Subtract the Numerators

Subtract the numerators: 126 - 22791 = -22665

Step 5: Simplify the Fraction

We can simplify \(\frac-22665642\) to its lowest form.
The greatest common divisor (GCD) of -22665 and 642 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-7555214\).

Step 6: Convert to Mixed Number

The fraction \(\frac-7555214\) can be written as the mixed number \(-36\frac149214\).

Final Answer

The result of 21/107 subtracted by 213/6 is:

\[ \frac{21}{107} - \frac{213}{6} = -36\frac149214 \]

Understanding Fraction Subtraction

How to Subtract Fractions

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

\( \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \) (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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