81/81 subtracted by 109/8 in Fraction Form

The result of 81/81 subtracted by 109/8 is: -13 3/8

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1098\) from \(\frac8181\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 81 and 8 is 648.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac8181\) to \(\frac{648}648\)
Convert \(\frac1098\) to \(\frac{8829}648\)

Step 4: Subtract the Numerators

Subtract the numerators: 648 - 8829 = -8181

Step 5: Simplify the Fraction

We can simplify \(\frac-8181648\) to its lowest form.
The greatest common divisor (GCD) of -8181 and 648 is 81.
Dividing both numerator and denominator by the GCD, we get \(\frac-1018\).

Step 6: Convert to Mixed Number

The fraction \(\frac-1018\) can be written as the mixed number \(-13\frac38\).

Final Answer

The result of 81/81 subtracted by 109/8 is:

\[ \frac{81}{81} - \frac{109}{8} = -13\frac38 \]

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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