Percentages
a. The labels on U-Turn protein energy bars include the statement that these bars contain “125% less fat than the leading chocolate candy brands” (based on data from Consumer Reports magazine). What is wrong with that claim?

Verified step by step guidance

1. Understand the concept of percentage reduction: A percentage reduction is calculated as the difference between the original and new values, divided by the original value, then multiplied by 100 to convert it to a percentage.
2. Recognize the logical flaw: A claim of '125% less fat' implies that the energy bars have negative fat content, which is not possible. Percentages over 100% in this context are nonsensical because they suggest a reduction greater than the total amount present.
3. Consider the correct interpretation: A more accurate claim would be that the energy bars have a certain percentage of the fat content of the leading chocolate candy brands, such as '75% less fat' if they contain 25% of the original fat content.
4. Evaluate the claim mathematically: If the leading chocolate candy brand has X grams of fat, a 125% reduction would imply the energy bars have X - 1.25X = -0.25X grams of fat, which is impossible.
5. Conclude with the correct approach: The claim should be revised to reflect a realistic and mathematically sound percentage reduction, ensuring it does not exceed 100%.

Key Concepts

Understanding Percentages

Percentages are a way to express a number as a fraction of 100, often used to compare proportions. When a claim states '125% less,' it implies a reduction greater than the original amount, which is mathematically impossible. Understanding how percentages work is crucial to identifying errors in such claims.

Interpreting Percentage Reductions

A percentage reduction indicates how much a quantity decreases relative to its original value. A claim of '125% less' suggests a complete reduction and then some, which is nonsensical. Typically, reductions are expressed as a percentage of the original, not exceeding 100%.

Misleading Advertising Claims

Misleading claims often use percentages to exaggerate benefits or differences. In this case, the claim of '125% less fat' is misleading because it suggests an impossible reduction. Recognizing such tactics is important for critically evaluating product information and advertisements.