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A direct prompt can be used to instruct a Large Language Model to perform a specific mathematical task. An example of such a prompt is the request: 'Please calculate the average of the numbers 2, 4, and 9.'

Example of a Prompt for a Direct Mathematical Calculation

The process to calculate the average of 2, 4, and 9 involves several distinct steps. First, the numbers are summed: $2 + 4 + 9 = 15$. Second, the quantity of numbers in the set is identified, which is three. Finally, the total sum is divided by this count to find the average: $15 / 3 = 5$. The resulting average is 5.

Step-by-Step Calculation of the Average of 2, 4, and 9

A user needs to find the total cost of three items priced at $4.50, $12.00, and $7.75. Write a single, self-contained prompt that directly instructs a language model to perform this specific mathematical calculation.

Crafting a Direct Calculation Prompt

A user needs to find the final price of a $60 item that has a 15% discount. The user gives the language model the following prompt: 'What should I know about a 15% discount on a $60 item?' The model responds by explaining what a discount is and how percentages work in general, but it does not give the final price. Evaluate the user's prompt. Why was it ineffective for getting a specific numerical answer?

Evaluating a Prompt for a Mathematical Task

When a Large Language Model is directly asked to calculate the average of the numbers $${}2$$, $${}4$$, and $${}9$$ without being provided any reasoning steps or demonstrations, it often struggles to arrive at the correct answer. In this zero-shot scenario, the model might incorrectly output an answer like $${}6$$, demonstrating that finding the correct mathematical solution directly is difficult without a step-by-step problem-solving path.

LLM's Answer ($${}6$$) to the Prompt for Calculating the Average of $${}2$$, $${}4$$, and $${}9$$

When a Large Language Model is prompted to calculate the average of the numbers 2, 4, and 9 using few-shot demonstrations that only contain question-answer pairs, it might provide the incorrect answer 7. The actual average is 5, calculated as $$(2+4+9)/3$$. This response illustrates that models can struggle to deduce multi-step mathematical reasoning without explicit step-by-step demonstrations.

LLM's Incorrect Answer (7) to the Prompt for Calculating the Average of 2, 4, and 9

A user wants a language model to determine a car's fuel efficiency, which is 150 miles driven using 5 gallons of gas. Which of the following prompts is best structured to request a direct and specific mathematical calculation from the model to find the answer?

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