78/155 subtracted by 154/4 in Fraction Form

The result of 78/155 subtracted by 154/4 is: -38 1/310

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1544\) from \(\frac78155\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 155 and 4 is 620.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac78155\) to \(\frac{312}620\)
Convert \(\frac1544\) to \(\frac{23870}620\)

Step 4: Subtract the Numerators

Subtract the numerators: 312 - 23870 = -23558

Step 5: Simplify the Fraction

We can simplify \(\frac-23558620\) to its lowest form.
The greatest common divisor (GCD) of -23558 and 620 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-11779310\).

Step 6: Convert to Mixed Number

The fraction \(\frac-11779310\) can be written as the mixed number \(-38\frac1310\).

Final Answer

The result of 78/155 subtracted by 154/4 is:

\[ \frac{78}{155} - \frac{154}{4} = -38\frac1310 \]

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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