209/133 subtracted by 185/4 in Fraction Form

The result of 209/133 subtracted by 185/4 is: -45 9/28

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1854\) from \(\frac209133\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 133 and 4 is 532.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac209133\) to \(\frac{836}532\)
Convert \(\frac1854\) to \(\frac{24605}532\)

Step 4: Subtract the Numerators

Subtract the numerators: 836 - 24605 = -23769

Step 5: Simplify the Fraction

We can simplify \(\frac-23769532\) to its lowest form.
The greatest common divisor (GCD) of -23769 and 532 is 19.
Dividing both numerator and denominator by the GCD, we get \(\frac-125128\).

Step 6: Convert to Mixed Number

The fraction \(\frac-125128\) can be written as the mixed number \(-45\frac928\).

Final Answer

The result of 209/133 subtracted by 185/4 is:

\[ \frac{209}{133} - \frac{185}{4} = -45\frac928 \]

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).

Fraction Calculator

Calculate operations between any two fractions: