64/305 subtracted by 128/4 in Fraction Form

The result of 64/305 subtracted by 128/4 is: -32 64/305

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1284\) from \(\frac64305\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 305 and 4 is 1220.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac64305\) to \(\frac{256}1220\)
Convert \(\frac1284\) to \(\frac{39040}1220\)

Step 4: Subtract the Numerators

Subtract the numerators: 256 - 39040 = -38784

Step 5: Simplify the Fraction

We can simplify \(\frac-387841220\) to its lowest form.
The greatest common divisor (GCD) of -38784 and 1220 is 4.
Dividing both numerator and denominator by the GCD, we get \(\frac-9696305\).

Step 6: Convert to Mixed Number

The fraction \(\frac-9696305\) can be written as the mixed number \(-32\frac64305\).

Final Answer

The result of 64/305 subtracted by 128/4 is:

\[ \frac{64}{305} - \frac{128}{4} = -32\frac64305 \]

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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