Algebraic addition
Algebraic addition is the technique of converting any subtraction problem into an addition problem by adding the opposite (additive inverse) of the number being subtracted. The problem a − b becomes a + (−b). For example, 8 − (−3) becomes 8 + 3 = 11, and −9 − 4 becomes −9 + (−4) = −13. This 7th grade math skill from Saxon Math Course 2 eliminates confusion with double negatives and is fundamental to simplifying algebraic expressions throughout pre-algebra and algebra.
Key Concepts
Property To use algebraic addition, treat subtraction as adding the opposite. The problem $a b$ becomes an addition problem: $a + ( b)$.
Examples $15 5$ can be solved by thinking $15 + ( 5) = 10$. $ 9 4$ is simplified by thinking $( 9) + ( 4) = 13$. $8 ( 3)$ becomes an addition problem: $8 + [ ( 3)] = 8 + 3 = 11$.
Explanation Think of this as a math superpower! Instead of taking numbers away, you can turn any subtraction problem into an addition party just by adding the opposite number. This trick makes simplifying expressions with lots of negative signs way easier to handle. It turns a confusing subtraction mess into a straightforward addition problem every single time.
Common Questions
What is algebraic addition?
Algebraic addition is the method of rewriting subtraction as adding the opposite. Instead of subtracting a number, you add its negative. So a − b = a + (−b).
How do I use algebraic addition to simplify expressions?
Rewrite every subtraction sign as adding the opposite of what follows. For example, −9 − 4 becomes −9 + (−4) = −13, and 8 − (−3) becomes 8 + 3 = 11.
Why does subtracting a negative give a positive?
Subtracting a negative is the same as adding its opposite, which is a positive number. So 8 − (−3) = 8 + 3 = 11. The two negatives cancel out.
When do students learn algebraic addition?
Algebraic addition is taught in 7th grade Saxon Math Course 2, Chapter 7. It is a key step toward working confidently with negative numbers in algebra.
What is the difference between algebraic addition and regular addition?
Regular addition combines two positive quantities. Algebraic addition works with signed numbers (positives and negatives) by converting subtraction to addition of the opposite, making it a unified operation.
What are common mistakes with algebraic addition?
Students often make errors with double negatives like −(−3). Remember that −(−3) = +3. Always rewrite the subtraction first, then combine the signs.