20/107 subtracted by 102/2 in Fraction Form

The result of 20/107 subtracted by 102/2 is: -51 20/107

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1022\) from \(\frac20107\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 107 and 2 is 214.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac20107\) to \(\frac{40}214\)
Convert \(\frac1022\) to \(\frac{10914}214\)

Step 4: Subtract the Numerators

Subtract the numerators: 40 - 10914 = -10874

Step 5: Simplify the Fraction

We can simplify \(\frac-10874214\) to its lowest form.
The greatest common divisor (GCD) of -10874 and 214 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-5437107\).

Step 6: Convert to Mixed Number

The fraction \(\frac-5437107\) can be written as the mixed number \(-51\frac20107\).

Final Answer

The result of 20/107 subtracted by 102/2 is:

\[ \frac{20}{107} - \frac{102}{2} = -51\frac20107 \]

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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