204/70 subtracted by 61/3 in Fraction Form
The result of 204/70 subtracted by 61/3 is: -18 61/105
Step-by-Step Solution
Step 1: Understand the Problem
We need to subtract the fraction \(\frac613\) from \(\frac20470\).
Step 2: Find the Least Common Multiple (LCM)
To subtract fractions, we need a common denominator. The LCM of 70 and 3 is 210.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac20470\) to \(\frac{612}210\)
Convert \(\frac613\) to \(\frac{4270}210\)
Step 4: Subtract the Numerators
Subtract the numerators: 612 - 4270 = -3658
Step 5: Simplify the Fraction
We can simplify \(\frac-3658210\) to its lowest form.
The greatest common divisor (GCD) of -3658 and 210 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-1829105\).
Step 6: Convert to Mixed Number
The fraction \(\frac-1829105\) can be written as the mixed number \(-18\frac61105\).
Final Answer
The result of 204/70 subtracted by 61/3 is:
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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