Why a negative times a negative is a positive | Pre-Algebra | Khan Academy

TL;DR

When multiplying negative numbers, the result follows the rule: a negative times a negative is positive, and a positive times a negative is negative.

Transcript

Lets say you are an Ancient Philosopher who was building up mathematics who was building mathematics from the ground up And you already have a reasonable of what a negative number could or should represent and you know how to add and subtract negative numbers But now you are faced with a conundrum What happens when you multiply negative numbers? Ei... Read More

Key Insights

• #️⃣ Multiplying a positive number and a negative number results in a negative number.
• #️⃣ Multiplying two negative numbers gives a positive number.
• ✖️ The distributive property can be applied to maintain consistency in the multiplication of negative numbers.
• 🪜 The intuition of repeatedly adding or subtracting a number helps in understanding the results of multiplication.

Questions & Answers

Q: What happens when you multiply a positive number by a negative number?

When you multiply a positive number by a negative number, the result is a negative number. For example, 5 times negative 3 equals negative 15. This is consistent with the idea of repeatedly adding a negative number to a positive number.

Q: What is the result when you multiply two negative numbers?

When you multiply two negative numbers, the result is a positive number. For instance, negative 2 times negative 6 equals positive 12. This can be understood by considering the idea of repeatedly adding a negative number to a negative number.

Q: How does the distributive property help in understanding multiplication of negative numbers?

The distributive property allows us to distribute a factor to each term within parentheses. By applying it to multiplication of negative numbers, we can maintain consistency with other properties of mathematics and derive the correct results.

Q: What is the intuition behind multiplying negative numbers?

The intuition behind multiplying negative numbers lies in the idea of repeatedly adding or subtracting a number. When multiplying a positive and a negative number, the result is negative because we are subtracting the positive number repeatedly. Conversely, when multiplying two negative numbers, the result is positive as we are subtracting the negative number repeatedly.

Summary & Key Takeaways

• Multiplying a positive number by a negative number results in a negative number, while multiplying a negative number by a positive number results in a negative number.

• The concept of multiplication of negative numbers can be understood by considering the distributive property and consistency with other properties of mathematics.

• Using thought experiments and intuition, it can be concluded that multiplying two negative numbers gives a positive result.