78/165 subtracted by 235/4 in Fraction Form

The result of 78/165 subtracted by 235/4 is: -59 159/220

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2354\) from \(\frac78165\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 165 and 4 is 660.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac78165\) to \(\frac{312}660\)
Convert \(\frac2354\) to \(\frac{38775}660\)

Step 4: Subtract the Numerators

Subtract the numerators: 312 - 38775 = -38463

Step 5: Simplify the Fraction

We can simplify \(\frac-38463660\) to its lowest form.
The greatest common divisor (GCD) of -38463 and 660 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-12821220\).

Step 6: Convert to Mixed Number

The fraction \(\frac-12821220\) can be written as the mixed number \(-59\frac159220\).

Final Answer

The result of 78/165 subtracted by 235/4 is:

\[ \frac{78}{165} - \frac{235}{4} = -59\frac159220 \]

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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