27/189 subtracted by 127/3 in Fraction Form

The result of 27/189 subtracted by 127/3 is: -43 17/21

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1273\) from \(\frac27189\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 189 and 3 is 189.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac27189\) to \(\frac{27}189\)
Convert \(\frac1273\) to \(\frac{8001}189\)

Step 4: Subtract the Numerators

Subtract the numerators: 27 - 8001 = -7974

Step 5: Simplify the Fraction

We can simplify \(\frac-7974189\) to its lowest form.
The greatest common divisor (GCD) of -7974 and 189 is 9.
Dividing both numerator and denominator by the GCD, we get \(\frac-88621\).

Step 6: Convert to Mixed Number

The fraction \(\frac-88621\) can be written as the mixed number \(-43\frac1721\).

Final Answer

The result of 27/189 subtracted by 127/3 is:

\[ \frac{27}{189} - \frac{127}{3} = -43\frac1721 \]

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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