102/87 subtracted by 170/4 in Fraction Form

The result of 102/87 subtracted by 170/4 is: -42 39/58

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1704\) from \(\frac10287\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 87 and 4 is 348.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac10287\) to \(\frac{408}348\)
Convert \(\frac1704\) to \(\frac{14790}348\)

Step 4: Subtract the Numerators

Subtract the numerators: 408 - 14790 = -14382

Step 5: Simplify the Fraction

We can simplify \(\frac-14382348\) to its lowest form.
The greatest common divisor (GCD) of -14382 and 348 is 6.
Dividing both numerator and denominator by the GCD, we get \(\frac-239758\).

Step 6: Convert to Mixed Number

The fraction \(\frac-239758\) can be written as the mixed number \(-42\frac3958\).

Final Answer

The result of 102/87 subtracted by 170/4 is:

\[ \frac{102}{87} - \frac{170}{4} = -42\frac3958 \]

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).

Fraction Calculator

Calculate operations between any two fractions: