51/81 subtracted by 81/3 in Fraction Form

The result of 51/81 subtracted by 81/3 is: -27 17/27

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac813\) from \(\frac5181\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 81 and 3 is 81.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac5181\) to \(\frac{51}81\)
Convert \(\frac813\) to \(\frac{2187}81\)

Step 4: Subtract the Numerators

Subtract the numerators: 51 - 2187 = -2136

Step 5: Simplify the Fraction

We can simplify \(\frac-213681\) to its lowest form.
The greatest common divisor (GCD) of -2136 and 81 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-71227\).

Step 6: Convert to Mixed Number

The fraction \(\frac-71227\) can be written as the mixed number \(-27\frac1727\).

Final Answer

The result of 51/81 subtracted by 81/3 is:

\[ \frac{51}{81} - \frac{81}{3} = -27\frac1727 \]

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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