182/40 subtracted by 174/2 in Fraction Form

The result of 182/40 subtracted by 174/2 is: -83 11/20

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1742\) from \(\frac18240\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 40 and 2 is 40.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac18240\) to \(\frac{182}40\)
Convert \(\frac1742\) to \(\frac{3480}40\)

Step 4: Subtract the Numerators

Subtract the numerators: 182 - 3480 = -3298

Step 5: Simplify the Fraction

We can simplify \(\frac-329840\) to its lowest form.
The greatest common divisor (GCD) of -3298 and 40 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac-164920\).

Step 6: Convert to Mixed Number

The fraction \(\frac-164920\) can be written as the mixed number \(-83\frac1120\).

Final Answer

The result of 182/40 subtracted by 174/2 is:

\[ \frac{182}{40} - \frac{174}{2} = -83\frac1120 \]

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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