69/78 subtracted by 211/4 in Fraction Form

The result of 69/78 subtracted by 211/4 is: -52 7/52

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2114\) from \(\frac6978\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 78 and 4 is 156.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac6978\) to \(\frac{138}156\)
Convert \(\frac2114\) to \(\frac{8229}156\)

Step 4: Subtract the Numerators

Subtract the numerators: 138 - 8229 = -8091

Step 5: Simplify the Fraction

We can simplify \(\frac-8091156\) to its lowest form.
The greatest common divisor (GCD) of -8091 and 156 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-269752\).

Step 6: Convert to Mixed Number

The fraction \(\frac-269752\) can be written as the mixed number \(-52\frac752\).

Final Answer

The result of 69/78 subtracted by 211/4 is:

\[ \frac{69}{78} - \frac{211}{4} = -52\frac752 \]

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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