134/314 subtracted by 49/3 in Fraction Form

The result of 134/314 subtracted by 49/3 is: -16 44/471

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac493\) from \(\frac134314\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 314 and 3 is 942.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac134314\) to \(\frac{402}942\)
Convert \(\frac493\) to \(\frac{15386}942\)

Step 4: Subtract the Numerators

Subtract the numerators: 402 - 15386 = -14984

Step 5: Simplify the Fraction

We can simplify \(\frac-14984942\) to its lowest form.
The greatest common divisor (GCD) of -14984 and 942 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-7492471\).

Step 6: Convert to Mixed Number

The fraction \(\frac-7492471\) can be written as the mixed number \(-16\frac44471\).

Final Answer

The result of 134/314 subtracted by 49/3 is:

\[ \frac{134}{314} - \frac{49}{3} = -16\frac44471 \]

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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