A fraction 3/5 decreased by2/5. The resulting fraction is then increased by 20%. What is the percentage decrease/increase in the value original fraction?

Let's solve the problem using the given values.

### Step 1: Original Fraction
The original fraction is \( \frac{3}{5} \).

### Step 2: Decrease by \( \frac{2}{5} \)
We are instructed to decrease the original fraction \( \frac{3}{5} \) by \( \frac{2}{5} \).

The new fraction after the decrease is:
\[
\text{New Fraction} = \frac{3}{5} - \frac{2}{5} = \frac{1}{5}
\]

### Step 3: Increase by 20%
Next, we increase the resulting fraction \( \frac{1}{5} \) by 20%.

The new fraction after the increase is:
\[
\text{Final Fraction} = \frac{1}{5} \times 1.2 = \frac{1 \times 1.2}{5} = \frac{1.2}{5} = \frac{12}{50} = \frac{6}{25}
\]

### Step 4: Compare the Final Value with the Original Value
Now, let's calculate the percentage change from the original fraction \( \frac{3}{5} \) to the final fraction \( \frac{6}{25} \).

First, express both fractions with a common denominator:
\[
\frac{3}{5} = \frac{15}{25}, \quad \frac{6}{25} = \frac{6}{25}
\]

The percentage change is given by:
\[
\text{Percentage Change} = \frac{\text{Final Fraction} - \text{Original Fraction}}{\text{Original Fraction}} \times 100
\]

Substituting the values:
\[
\text{Percentage Change} = \frac{\frac{6}{25} - \frac{15}{25}}{\frac{15}{25}} \times 100 = \frac{\frac{6 - 15}{25}}{\frac{15}{25}} \times 100 = \frac{-9}{15} \times 100 = -60\%
\]

### Final Result:
The percentage change in the value of the original fraction is a **60% decrease**.

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Would you like more details or have any questions?

Here are 5 related questions:
1. What happens if the decrease was \( \frac{1}{5} \) instead of \( \frac{2}{5} \)?
2. How does the percentage change vary if the increase was 10% instead of 20%?
3. What is the final fraction if the original fraction was increased by 20% instead of decreased first?
4. How does the change affect the final value if the original fraction is \( \frac{4}{5} \) instead of \( \frac{3}{5} \)?
5. What would the percentage change be if the fraction was decreased by \( \frac{4}{5} \) instead of \( \frac{2}{5} \)?

**Tip:** When working with fractions, converting them to have a common denominator can simplify the process of comparing their values.

Explore how to calculate the percentage change of fractions step-by-step. Given the fraction 3/5 decreased by 2/5 and then increased by 20%, find the percentage change in the value of the original fraction. Learn with detailed explanations and calculations.

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