140/129 subtracted by 233/3 in Fraction Form

The result of 140/129 subtracted by 233/3 is: -77 18/43

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2333\) from \(\frac140129\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 129 and 3 is 129.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac140129\) to \(\frac{140}129\)
Convert \(\frac2333\) to \(\frac{10019}129\)

Step 4: Subtract the Numerators

Subtract the numerators: 140 - 10019 = -9879

Step 5: Simplify the Fraction

We can simplify \(\frac-9879129\) to its lowest form.
The greatest common divisor (GCD) of -9879 and 129 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-329343\).

Step 6: Convert to Mixed Number

The fraction \(\frac-329343\) can be written as the mixed number \(-77\frac1843\).

Final Answer

The result of 140/129 subtracted by 233/3 is:

\[ \frac{140}{129} - \frac{233}{3} = -77\frac1843 \]

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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