Subtraction as Adding the Opposite
Subtraction as adding the opposite is a Grade 6 integer skill in Big Ideas Math Advanced 1, Chapter 11: Integers. This concept teaches that any subtraction expression can be rewritten as adding the additive inverse — converting a - b into a + (-b). This rule applies to all integers and simplifies solving integer subtraction problems.
Key Concepts
Subtraction of integers is the same as adding the additive inverse, so $p q = p + ( q)$. A number and its opposite have a sum of 0 and are called additive inverses. The opposite of $a$ is written as $ a$.
Common Questions
What is the rule for subtraction as adding the opposite?
The rule states that a - b = a + (-b) for all integers. Instead of subtracting, you change the subtraction sign to addition and take the opposite (negative) of the number being subtracted.
Why does subtracting equal adding the opposite?
Every number has an additive inverse (its opposite), and adding the inverse produces the same result as subtracting. This is a fundamental property of integers that simplifies calculations.
How does this rule work with negative numbers?
When subtracting a negative number, you add its opposite, which is positive. For example, 6 - (-4) = 6 + 4 = 10. Subtracting a negative always results in a larger value.
Where is integer subtraction taught in Big Ideas Math Advanced 1?
Subtraction as adding the opposite is covered in Chapter 11: Integers of Big Ideas Math Advanced 1, the Grade 6 math textbook.