Concept: Subtracting by Adding the Opposite
Subtracting by adding the opposite is a core integer concept in Grade 6 math, covered in Big Ideas Math Advanced 1, Chapter 13: Expressions and Equations. The rule states that subtracting a number is the same as adding its additive inverse — for example, 5 - 3 equals 5 + (-3). This concept allows subtraction of integers to be rewritten as addition, simplifying calculations.
Key Concepts
When subtracting linear expressions, you can rewrite subtraction as adding the opposite (additive inverse). For any linear expressions $A$ and $B$, we have $A B = A + ( B)$. The opposite of an expression changes the sign of every term.
Common Questions
What does "subtracting by adding the opposite" mean?
It means rewriting any subtraction problem as an addition problem by changing the sign of the number being subtracted. For example, 8 - 3 becomes 8 + (-3), and both give the same answer of 5.
Why do we add the opposite when subtracting integers?
Adding the opposite (additive inverse) transforms subtraction into addition, which is easier to handle with negative numbers. The rule a - b = a + (-b) works for all integers, including negative numbers.
How does subtracting by adding the opposite work with negative integers?
When subtracting a negative integer, you add its opposite (a positive number). For example, 4 - (-3) becomes 4 + 3 = 7. Subtracting a negative always increases the value.
Where is this concept taught in Big Ideas Math Advanced 1?
Subtracting by adding the opposite is covered in Chapter 13: Expressions and Equations of Big Ideas Math Advanced 1, the Grade 6 math textbook.