Thinking about the sign of expressions | 7th grade | Khan Academy

TL;DR

When multiplying or dividing positive and negative numbers together, the sign of the expression depends on the number of negative factors and the positioning of the negative sign.

Transcript

• [Voiceover] Let's now do some examples that test our understanding of what happens when we multiply or divide a bunch of positive or negative numbers together. And like always, pause the video and see if you can work through it on your own before I do it. So first question: What is the sign of s to the 67th power divided by t to the ninth power, ... Read More

Key Insights

• ❎ Negative numbers multiplied together result in a positive product if the number of negative factors is even.
• ✊ A positive number to any power is always positive, regardless of the exponent.
• ❎ Dividing a negative number by a positive number yields a negative quotient.
• 0️⃣ Multiplying or dividing any numbers by zero always results in a product or quotient of zero.

Questions & Answers

Q: What happens when you multiply or divide a negative number by an odd number of negative numbers?

When you multiply or divide a negative number by an odd number of negative numbers, the product or quotient will be negative. This is because an odd number of negatives multiplied together results in a negative product.

Q: What is the sign of a positive number to any power?

A positive number to any power, whether it is even or odd, will always be positive. The exponent does not affect the sign of a positive number.

Q: What is the result when you divide a negative number by a positive number?

When you divide a negative number by a positive number, the result is always negative. This is because dividing a negative number by a positive number is equivalent to multiplying by a negative reciprocal.

Q: What is the sign of a product or quotient when one of the factors is zero?

When one of the factors in a product or quotient is zero, the entire expression will be equal to zero. This is because anything multiplied or divided by zero is always zero.

Q: How does the positioning of the negative sign affect the sign of the expression?

The positioning of the negative sign can change the overall sign of the expression. When negative numbers are multiplied together, the sign depends on whether the negative sign is within the parentheses or in front of the entire expression.

Summary & Key Takeaways

• Multiplying or dividing a negative number by an odd number of negative numbers results in a negative product, while multiplying by an even number of negative numbers produces a positive product.

• A positive number to any power is always positive, and a negative divided by a positive is negative.

• Multiplying any numbers by zero always results in a product of zero.

• When negative numbers are multiplied together, the overall sign depends on the positioning of the negative sign.