154/77 subtracted by 101/6 in Fraction Form

The result of 154/77 subtracted by 101/6 is: -15 1/6

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1016\) from \(\frac15477\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 77 and 6 is 462.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac15477\) to \(\frac{924}462\)
Convert \(\frac1016\) to \(\frac{7777}462\)

Step 4: Subtract the Numerators

Subtract the numerators: 924 - 7777 = -6853

Step 5: Simplify the Fraction

We can simplify \(\frac-6853462\) to its lowest form.
The greatest common divisor (GCD) of -6853 and 462 is 77.
Dividing both numerator and denominator by the GCD, we get \(\frac-896\).

Step 6: Convert to Mixed Number

The fraction \(\frac-896\) can be written as the mixed number \(-15\frac16\).

Final Answer

The result of 154/77 subtracted by 101/6 is:

\[ \frac{154}{77} - \frac{101}{6} = -15\frac16 \]

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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