102/118 subtracted by 86/2 in Fraction Form

The result of 102/118 subtracted by 86/2 is: -43 51/59

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac862\) from \(\frac102118\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 118 and 2 is 118.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac102118\) to \(\frac{102}118\)
Convert \(\frac862\) to \(\frac{5074}118\)

Step 4: Subtract the Numerators

Subtract the numerators: 102 - 5074 = -4972

Step 5: Simplify the Fraction

We can simplify \(\frac-4972118\) to its lowest form.
The greatest common divisor (GCD) of -4972 and 118 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-248659\).

Step 6: Convert to Mixed Number

The fraction \(\frac-248659\) can be written as the mixed number \(-43\frac5159\).

Final Answer

The result of 102/118 subtracted by 86/2 is:

\[ \frac{102}{118} - \frac{86}{2} = -43\frac5159 \]

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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