27/123 subtracted by 233/4 in Fraction Form

The result of 27/123 subtracted by 233/4 is: -59 159/164

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2334\) from \(\frac27123\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 123 and 4 is 492.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac27123\) to \(\frac{108}492\)
Convert \(\frac2334\) to \(\frac{28659}492\)

Step 4: Subtract the Numerators

Subtract the numerators: 108 - 28659 = -28551

Step 5: Simplify the Fraction

We can simplify \(\frac-28551492\) to its lowest form.
The greatest common divisor (GCD) of -28551 and 492 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-9517164\).

Step 6: Convert to Mixed Number

The fraction \(\frac-9517164\) can be written as the mixed number \(-59\frac159164\).

Final Answer

The result of 27/123 subtracted by 233/4 is:

\[ \frac{27}{123} - \frac{233}{4} = -59\frac159164 \]

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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