How to Simplify Expressions Using Properties of Addition

TL;DR

Subtraction can be simplified by rewriting it as adding the opposite, allowing the use of associative and commutative properties. This method streamlines expressions, making calculations more efficient and demonstrating the importance of understanding these mathematical properties.

Transcript

• [Instructor] What we're going to do in this video is evaluate this pretty hairy expression and we could just try to do it. We could go from left to right, but it feels like there might be a simpler way to do it. I'm adding 13 here and then I'm subtracting 13. I'm, I have a negative five here and then I have a positive five. You might be tempted t... Read More

Key Insights

• ❓ The commutative property applies to addition but not subtraction.
• 🪜 Subtraction can be rewritten as adding the opposite of a number.
• 😒 Rewriting subtraction as addition allows for the use of the commutative and associative properties.
• 😑 Simplifying expressions through rewriting subtraction as addition can make calculations easier and more efficient.
• 😑 The process of simplifying expressions through rewriting subtraction as addition is a valuable skill in mathematics.
• 😑 Exploring different approaches to evaluating expressions can lead to more efficient problem-solving.
• 😑 The commutative property allows for the changing of the order of addition, leading to simplified expressions.

Questions & Answers

Q: Why can't the commutative property be applied to subtraction?

The commutative property only applies to addition, as changing the order of subtraction does not lead to the same result. For example, 9 minus 7 is not equal to 7 minus 9.

Q: How can subtraction be rewritten as addition?

Subtraction can be rewritten as adding the opposite of a number. For instance, 6 minus 3 is the same as adding the opposite of 3, which is -3.

Q: How does rewriting subtraction as addition help simplify expressions?

By rewriting subtraction as addition, one can use the commutative property to change the order of addition. This allows for easier pairing and cancellation of opposites, simplifying the expression.

Q: Can the associative property be used when rewriting subtraction as addition?

Yes, the associative property can be used. Pairing numbers and grouping them in parentheses can help simplify expressions further by identifying and canceling out opposites.

Summary & Key Takeaways

• The commutative property applies to addition, allowing the order of addition to be changed, but it does not apply to subtraction.

• Subtraction can be rewritten as adding the opposite of a number.

• By rewriting subtraction as addition, the commutative and associative properties can be used to simplify expressions.