67/61 subtracted by 214/2 in Fraction Form
The result of 67/61 subtracted by 214/2 is: -106 6/61
Step-by-Step Solution
Step 1: Understand the Problem
We need to subtract the fraction \(\frac2142\) from \(\frac6761\).
Step 2: Find the Least Common Multiple (LCM)
To subtract fractions, we need a common denominator. The LCM of 61 and 2 is 122.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac6761\) to \(\frac{134}122\)
Convert \(\frac2142\) to \(\frac{13054}122\)
Step 4: Subtract the Numerators
Subtract the numerators: 134 - 13054 = -12920
Step 5: Simplify the Fraction
We can simplify \(\frac-12920122\) to its lowest form.
The greatest common divisor (GCD) of -12920 and 122 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-646061\).
Step 6: Convert to Mixed Number
The fraction \(\frac-646061\) can be written as the mixed number \(-106\frac661\).
Final Answer
The result of 67/61 subtracted by 214/2 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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