105/51 subtracted by 256/4 in Fraction Form

The result of 105/51 subtracted by 256/4 is: -62 1/17

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2564\) from \(\frac10551\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 51 and 4 is 204.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac10551\) to \(\frac{420}204\)
Convert \(\frac2564\) to \(\frac{13056}204\)

Step 4: Subtract the Numerators

Subtract the numerators: 420 - 13056 = -12636

Step 5: Simplify the Fraction

We can simplify \(\frac-12636204\) to its lowest form.
The greatest common divisor (GCD) of -12636 and 204 is 12.
Dividing both numerator and denominator by the GCD, we get \(\frac-105317\).

Step 6: Convert to Mixed Number

The fraction \(\frac-105317\) can be written as the mixed number \(-62\frac117\).

Final Answer

The result of 105/51 subtracted by 256/4 is:

\[ \frac{105}{51} - \frac{256}{4} = -62\frac117 \]

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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