Table of Contents

Using a multiplier Level 8

Introduction

Have you ever wondered how much a product’s price changes during a sale? Or how to determine the increase in your favorite video game’s price over time? Learning to use a multiplier to calculate percentage changes will help you answer these questions and more! Understanding this concept is crucial in math and everyday life, especially in finance and budgeting.

Definition and Concept

A multiplier is a number used to increase or decrease another number by a certain percentage. When calculating percentage changes, we often express the change as a multiplier that can be applied to the original amount. For example, if a price increases by 20%, the multiplier would be 1.20, while a decrease of 15% would use a multiplier of 0.85.

Relevance:

  • Mathematics: Understanding multipliers is essential for mastering percentages, ratios, and proportions.
  • Real-world applications: Used in finance, sales, and everyday decision-making.

Historical Context or Origin​

The concept of percentages dates back to ancient civilizations, including the Babylonians and Egyptians, who used fractions to represent parts of a whole. The modern use of percentages and multipliers became more standardized in the 16th century, as trade and commerce expanded, necessitating more precise calculations for profit and loss.

Understanding the Problem

To calculate percentage changes using a multiplier, you need to know the original amount and the percentage change. Let’s break this down using an example:
Example Problem: Calculate the new price of a jacket that originally costs $50 with a 20% increase.

  • Identify the original price ($50) and the percentage increase (20%).
  • Convert the percentage to a decimal (20% = 0.20).

Methods to Solve the Problem with different types of problems​

Method 1: Using the Multiplier Directly

  • Convert the percentage to a multiplier: For a 20% increase, the multiplier is 1.20.
  • Multiply the original amount by the multiplier: $50 x 1.20 = $60.

    • Example:
    Calculate the new price of a $40 shirt after a 15% decrease.

  • Convert 15% to a multiplier: 0.85.
  • Multiply: $40 x 0.85 = $34.

    • Method 2: Step-by-Step Calculation

  • Calculate the percentage amount separately, then add or subtract it from the original amount.

    • Example:
    Find the new price of a $70 item after a 25% increase.

  • Calculate 25% of $70: $70 x 0.25 = $17.50.
  • Add this to the original price: $70 + $17.50 = $87.50.

    • Exceptions and Special Cases​

  • Negative Percentage Changes: When the percentage is negative, it represents a decrease. For example, a 10% decrease in a $100 item would use a multiplier of 0.90.
  • Zero Percentage Changes: If the percentage change is 0%, the original amount remains unchanged regardless of the multiplier.

    • Step-by-Step Practice​

    Problem 1: Calculate the new price of a $80 item after a 30% increase.

    Solution:

  • Multiplier: 1.30.
  • Calculation: $80 x 1.30 = $104.

    • Problem 2: Find the new price of a $60 item after a 10% decrease.

    Solution:

    1. Multiplier: 0.90.
    2. Calculation: $60 x 0.90 = $54.

    Same Problem Statement With Different Methods:
    Calculate the new price of a $100 item after a 20% increase.

    Method 1: Using the Multiplier

    1. Multiplier: 1.20.
    2. Calculation: $100 x 1.20 = $120.

    Method 2: Step-by-Step Calculation

    1. Calculate 20% of $100: $100 x 0.20 = $20.
    2. Add to original price: $100 + $20 = $120.

    Examples and Variations

    Easy Example:

    • Problem: Calculate the new price of a $50 item after a 10% increase.
    • Solution:
      • Multiplier: 1.10.
      • Calculation: $50 x 1.10 = $55.

    Moderate Example:

    • Problem: Find the new price of a $120 item after a 25% decrease.
    • Solution:
      • Multiplier: 0.75.
      • Calculation: $120 x 0.75 = $90.

    Advanced Example:

    • Problem: Calculate the price change of a $200 item after a 15% increase followed by a 10% decrease.
    • Solution:
      • First increase: Multiplier 1.15; $200 x 1.15 = $230.
      • Then decrease: Multiplier 0.90; $230 x 0.90 = $207.

    Interactive Quiz with Feedback System​

    You do not have access to this page.

    If you are not a subscriber, please click here to subscribe.
    OR

    Common Mistakes and Pitfalls

    • Confusing how to convert percentages into multipliers.
    • Forgetting to apply the correct multiplier for increases vs. decreases.
    • Not checking calculations for accuracy.

    Tips and Tricks for Efficiency

    • Always convert percentages to decimals before finding multipliers.
    • Double-check your work by calculating the percentage amount separately.
    • Use estimation to quickly assess if your final answer makes sense.

    Real life application

    • Finance: Understanding discounts during sales or price increases for budgeting.
    • Shopping: Calculating final prices after applying discounts.
    • Investments: Evaluating percentage changes in stock prices or savings accounts.

    FAQ's

    A negative percentage indicates a decrease. Use a multiplier less than 1 to find the new amount.
    Yes, multipliers can be used for any percentage, whether it’s an increase or decrease.
    Use the formula: Percentage Change = (New Value – Old Value) / Old Value x 100%.
    Yes, multipliers greater than 2 indicate a percentage increase of more than 100%.
    They simplify calculations for percentage changes, making it easier to understand financial aspects in real life.

    Conclusion

    Using a multiplier to calculate percentage changes is a vital skill that can help you in various real-life situations, from shopping to budgeting. By mastering this concept, you’ll be better equipped to handle financial decisions and understand changes in prices effectively.

    References and Further Exploration

    • Khan Academy: Interactive lessons on percentages and multipliers.
    • Book: Mathematics for Everyday Life by John Doe.

    Like? Share it with your friends

    Facebook
    Twitter
    LinkedIn

    Filter

    • Category

    • Levels

    • Subject