78/87 subtracted by 11/4 in Fraction Form
The result of 78/87 subtracted by 11/4 is: -2 17/116
Step-by-Step Solution
Step 1: Understand the Problem
We need to subtract the fraction \(\frac114\) from \(\frac7887\).
Step 2: Find the Least Common Multiple (LCM)
To subtract fractions, we need a common denominator. The LCM of 87 and 4 is 348.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac7887\) to \(\frac{312}348\)
Convert \(\frac114\) to \(\frac{957}348\)
Step 4: Subtract the Numerators
Subtract the numerators: 312 - 957 = -645
Step 5: Simplify the Fraction
We can simplify \(\frac-645348\) to its lowest form.
The greatest common divisor (GCD) of -645 and 348 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac-215116\).
Step 6: Convert to Mixed Number
The fraction \(\frac-215116\) can be written as the mixed number \(-2\frac17116\).
Final Answer
The result of 78/87 subtracted by 11/4 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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