Percentage Increase Practice Flashcards

Learning Objective

• The primary goal is to solve problems involving percentage increase through various mathematical methods and real-world scenarios.

recap: Equivalencies between Fractions, Decimals, and Percents

Understanding the relationship between these three forms is essential for calculating percentage increases.

• $\frac{3}{4} = 0.75 = 75\%$

• $\frac{1}{4} = 0.25 = 25\%$

• $\frac{1}{2} = 0.5 = 50\%$

• $\frac{1}{1} = 1.0 = 100\%$

• $0 = 0.0 = 0\%$

Defining Percentage Increase

• Definition: Percentage increase measures the amount of growth or increase in comparison to the original value, expressed as a percentage.

• Formula: $\text{Percentage Increase} = \frac{\text{Amount of Increase}}{\text{Original Value}} \times 100\%$

• Expanded Formula: $\text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%$

Illustrative Situation: Back-to-School Notebook Product

• Scenario: At the start of the season, a notebook costs $\text{₱}20.00$. A salesman states the price will rise to $\text{₱}28.00$ next week, claiming this is a $30\%$ increase in the product price.

• Checking the Claim:

  • Change Type: Increase.

  • Amount of Increase: $\text{₱}28.00 - \text{₱}20.00 = \text{₱}8.00$.

  • Calculating 30% of the Original: $0.30 \times 20 = 6$. Since the actual increase is $8$, the salesman's claim of a $30\%$ increase is mathematically incorrect.

• Calculating the True Percentage Increase:

  • Original Value: $20$

  • New Value: $28$

  • Calculation: $\frac{28 - 20}{20} \times 100\% = \frac{8}{20} \times 100\%$

  • Long Division: $8 \div 20 = 0.4$

  • Final Conversion: $0.4 \times 100 = 40\%$

  • Result: The actual percentage increase is $40\%$.

Activity A: Table of Percentage Increase Calculations

This activity compares original and new values to determine the exact percentage of growth.

• Example 1:

  • Original: $100$

  • New: $120$

  • Increase: $120 - 100 = 20$

  • Calculation: $\frac{20}{100} = 0.20 \times 100 = 20\%$

• Example 2:

  • Original: $250$

  • New: $400$

  • Increase: $400 - 250 = 150$

  • Calculation: $\frac{150}{250} = 0.6 \times 100 = 60\%$

• Example 3:

  • Original: $65$

  • New: $74.75$

  • Increase: $74.75 - 65 = 9.75$

  • Calculation: $\frac{9.75}{65} = 0.15 \times 100 = 15\%$

• Example 4:

  • Original: $180$

  • New: $225$

  • Increase: $225 - 180 = 45$

  • Calculation: $\frac{45}{180} = 0.25 \times 100 = 25\%$

• Example 5:

  • Original: $199$

  • New: $298.5$

  • Increase: $298.5 - 199 = 99.5$

  • Calculation: $\frac{99.5}{199} = 0.5 \times 100 = 50\%$

Activity B: Solving for Unknown Variables

This section involves finding the missing piece (Original, New, or Percent) based on the provided data.

• Case 1:

  • Original: $40$

  • New: $50$

  • Increase: $50 - 40 = 10$

  • Percentage Increase: $\frac{10}{40} = 0.25 \times 100 = 25\%$

• Case 2:

  • Original: $190$

  • Percentage Increase: $45\% \text{ (or } 0.45)$

  • Finding the Increase: $0.45 \times 190 = 85.5$

  • Finding the New Value: $190 + 85.5 = 275.5$

• Case 3:

  • Original: $75$

  • Percentage Increase: $12\% \text{ (or } 0.12)$

  • Finding the Increase: $0.12 \times 75 = 9$

  • Finding the New Value: $75 + 9 = 84$

• Case 4:

  • New Value: $374.4$

  • Increase Amount: $54.4$

  • Finding the Original Value: $374.4 - 54.4 = 320$

  • Percentage Increase: $\frac{54.4}{320} = 0.17 \times 100 = 17\%$

• Case 5:

  • New Value: $873.25$

  • Increase Amount: $374.25$

  • Finding the Original Value: $873.25 - 374.25 = 499$

  • Percentage Increase: $\frac{374.25}{499} = 0.75 \times 100 = 75\%$

Problem Solving Examples

• Example 2 (Fast Food Sales):

  • Context: A restaurant recorded $\text{₱}250,000$ sales in week one and $\text{₱}320,000$ in week two.

  • Solution: $\frac{320,000 - 250,000}{250,000} \times 100 = \frac{70,000}{250,000} \times 100$

  • Calculation: $0.28 \times 100 = 28\%$

  • Long Division Reference: $70,000 \div 250,000 = 0.28$.

• Example 3 (Gasoline Price Adjustment):

  • Context: Original price was $\text{₱}67.00$ per liter. It adjusted to $\text{₱}68.34$.

  • Solution: $\frac{68.34 - 67}{67} \times 100 = \frac{1.34}{67} \times 100$

  • Calculation: $0.02 \times 100 = 2\%$

Activity C: Advanced Word Problems

• Problem 1 (University Enrollees):

  • Data: $2,350$ enrollees in 2023; $3,337$ enrollees in 2024.

  • Solution: $\frac{3,337 - 2,350}{2,350} \times 100 = \frac{987}{2,350} \times 100$

  • Result: $0.42 \times 100 = 42\%$

• Problem 2 (Smartphone Price Increase):

  • Data: The price became $\text{₱}13,000.00$ after a $\text{₱}1,000.00$ increase.

  • Step 1 (Find Original Price): $\text{Original Price} = 13,000 - 1,000 = 12,000$

  • Step 2 (Find Percentage): $\frac{1,000}{12,000} \times 100 = 0.08333... \times 100$

  • Result: $8.33\%$ (or rounded to $8.3\%$—note that transcript shows both $8.33\%$ and $8.3\%$—corrected calculation is $8.3\%$.

• Problem 3 (Lisa's Math Exercises):

  • Data: First attempt score was $45$; Second attempt was $58$.

  • Criterion: Must achieve at least a $30\%$ increase to proceed to the next set.

  • Solution: $\frac{58 - 45}{45} \times 100 = \frac{13}{45} \times 100$

  • Calculation: $0.2888... \times 100 = 28.89\%$

  • Decision: Since 28.89\% < 30\%, Lisa cannot proceed to the next set of exercises.