69/315 subtracted by 127/4 in Fraction Form

The result of 69/315 subtracted by 127/4 is: -32 197/420

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1274\) from \(\frac69315\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 315 and 4 is 1260.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac69315\) to \(\frac{276}1260\)
Convert \(\frac1274\) to \(\frac{40005}1260\)

Step 4: Subtract the Numerators

Subtract the numerators: 276 - 40005 = -39729

Step 5: Simplify the Fraction

We can simplify \(\frac-397291260\) to its lowest form.
The greatest common divisor (GCD) of -39729 and 1260 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-13243420\).

Step 6: Convert to Mixed Number

The fraction \(\frac-13243420\) can be written as the mixed number \(-32\frac197420\).

Final Answer

The result of 69/315 subtracted by 127/4 is:

\[ \frac{69}{315} - \frac{127}{4} = -32\frac197420 \]

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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