82/369 subtracted by 17/4 in Fraction Form

The result of 82/369 subtracted by 17/4 is: -5 35/36

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac174\) from \(\frac82369\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 369 and 4 is 1476.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac82369\) to \(\frac{328}1476\)
Convert \(\frac174\) to \(\frac{6273}1476\)

Step 4: Subtract the Numerators

Subtract the numerators: 328 - 6273 = -5945

Step 5: Simplify the Fraction

We can simplify \(\frac-59451476\) to its lowest form.
The greatest common divisor (GCD) of -5945 and 1476 is 41.
Dividing both numerator and denominator by the GCD, we get \(\frac-14536\).

Step 6: Convert to Mixed Number

The fraction \(\frac-14536\) can be written as the mixed number \(-5\frac3536\).

Final Answer

The result of 82/369 subtracted by 17/4 is:

\[ \frac{82}{369} - \frac{17}{4} = -5\frac3536 \]

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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