Question

finding a percent of change identify the percent of change as an increase or a decrease. then find the percent of change. round to the nearest tenth of a percent if necessary. 24. \\(\frac{1}{4}\\) to \\(\frac{1}{2}\\) 25. \\(\frac{4}{5}\\) to \\(\frac{3}{5}\\) 26. \\(\frac{3}{8}\\) to \\(\frac{7}{8}\\) 27. \\(\frac{5}{4}\\) to \\(\frac{3}{8}\\) from 20 to 40 is a 100% increase.

Explanation:

Step1: Recall Percent Change Formula

The formula for percent change is $\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$. First, identify if it's an increase or decrease by comparing new and old values.

Step2: Problem 24: $\frac{1}{4}$ to $\frac{1}{2}$

• Old Value ($OV$) = $\frac{1}{4}$, New Value ($NV$) = $\frac{1}{2}$.
• Since $\frac{1}{2} > \frac{1}{4}$, it's an increase.
• Calculate change: $\frac{\frac{1}{2} - \frac{1}{4}}{\frac{1}{4}} \times 100\% = \frac{\frac{1}{4}}{\frac{1}{4}} \times 100\% = 1 \times 100\% = 100\%$.

Step3: Problem 25: $\frac{4}{5}$ to $\frac{3}{5}$

• $OV = \frac{4}{5}$, $NV = \frac{3}{5}$.
• Since $\frac{3}{5} < \frac{4}{5}$, it's a decrease.
• Calculate change: $\frac{\frac{3}{5} - \frac{4}{5}}{\frac{4}{5}} \times 100\% = \frac{-\frac{1}{5}}{\frac{4}{5}} \times 100\% = -\frac{1}{4} \times 100\% = -25\%$ (25% decrease).

Step4: Problem 26: $\frac{3}{8}$ to $\frac{7}{8}$

• $OV = \frac{3}{8}$, $NV = \frac{7}{8}$.
• Since $\frac{7}{8} > \frac{3}{8}$, it's an increase.
• Calculate change: $\frac{\frac{7}{8} - \frac{3}{8}}{\frac{3}{8}} \times 100\% = \frac{\frac{4}{8}}{\frac{3}{8}} \times 100\% = \frac{4}{3} \times 100\% \approx 133.3\%$.

Step5: Problem 27: $\frac{5}{4}$ to $\frac{3}{8}$

• $OV = \frac{5}{4} = \frac{10}{8}$, $NV = \frac{3}{8}$.
• Since $\frac{3}{8} < \frac{10}{8}$, it's a decrease.
• Calculate change: $\frac{\frac{3}{8} - \frac{10}{8}}{\frac{10}{8}} \times 100\% = \frac{-\frac{7}{8}}{\frac{10}{8}} \times 100\% = -\frac{7}{10} \times 100\% = -70\%$ (70% decrease).

Answer:

1. Increase, 100%
2. Decrease, 25%
3. Increase, ≈133.3%
4. Decrease, 70%