20/105 subtracted by 213/4 in Fraction Form

The result of 20/105 subtracted by 213/4 is: -54 79/84

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2134\) from \(\frac20105\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 105 and 4 is 420.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac20105\) to \(\frac{80}420\)
Convert \(\frac2134\) to \(\frac{22365}420\)

Step 4: Subtract the Numerators

Subtract the numerators: 80 - 22365 = -22285

Step 5: Simplify the Fraction

We can simplify \(\frac-22285420\) to its lowest form.
The greatest common divisor (GCD) of -22285 and 420 is 5.
Dividing both numerator and denominator by the GCD, we get \(\frac-445784\).

Step 6: Convert to Mixed Number

The fraction \(\frac-445784\) can be written as the mixed number \(-54\frac7984\).

Final Answer

The result of 20/105 subtracted by 213/4 is:

\[ \frac{20}{105} - \frac{213}{4} = -54\frac7984 \]

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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