22/340 subtracted by 102/3 in Fraction Form

The result of 22/340 subtracted by 102/3 is: -34 11/170

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction \(\frac1023\) from \(\frac22340\).

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 340 and 3 is 1020.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac22340\) to \(\frac{66}1020\)
Convert \(\frac1023\) to \(\frac{34680}1020\)

Step 4: Subtract the Numerators

Subtract the numerators: 66 - 34680 = -34614

Step 5: Simplify the Fraction

We can simplify \(\frac-346141020\) to its lowest form.
The greatest common divisor (GCD) of -34614 and 1020 is 6.
Dividing both numerator and denominator by the GCD, we get \(\frac-5769170\).

Step 6: Convert to Mixed Number

The fraction \(\frac-5769170\) can be written as the mixed number \(-34\frac11170\).

Final Answer

The result of 22/340 subtracted by 102/3 is:

\[ \frac{22}{340} - \frac{102}{3} = -34\frac11170 \]

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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