83/135 subtracted by 82/6 in Fraction Form

The result of 83/135 subtracted by 82/6 is: -14 128/135

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac826\) from \(\frac83135\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 135 and 6 is 270.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac83135\) to \(\frac{166}270\)
Convert \(\frac826\) to \(\frac{3690}270\)

Step 4: Subtract the Numerators

Subtract the numerators: 166 - 3690 = -3524

Step 5: Simplify the Fraction

We can simplify \(\frac-3524270\) to its lowest form.
The greatest common divisor (GCD) of -3524 and 270 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-1762135\).

Step 6: Convert to Mixed Number

The fraction \(\frac-1762135\) can be written as the mixed number \(-14\frac128135\).

Final Answer

The result of 83/135 subtracted by 82/6 is:

\[ \frac{83}{135} - \frac{82}{6} = -14\frac128135 \]

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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