61/103 subtracted by 210/3 in Fraction Form

The result of 61/103 subtracted by 210/3 is: -70 61/103

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac2103\) from \(\frac61103\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 103 and 3 is 309.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac61103\) to \(\frac{183}309\)
Convert \(\frac2103\) to \(\frac{21630}309\)

Step 4: Subtract the Numerators

Subtract the numerators: 183 - 21630 = -21447

Step 5: Simplify the Fraction

We can simplify \(\frac-21447309\) to its lowest form.
The greatest common divisor (GCD) of -21447 and 309 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-7149103\).

Step 6: Convert to Mixed Number

The fraction \(\frac-7149103\) can be written as the mixed number \(-70\frac61103\).

Final Answer

The result of 61/103 subtracted by 210/3 is:

\[ \frac{61}{103} - \frac{210}{3} = -70\frac61103 \]

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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