Subtracting Integers by Adding the Opposite
Subtracting Integers by Adding the Opposite is a Grade 7 math skill in Illustrative Mathematics, Chapter 5: Rational Number Arithmetic. Students learn that subtracting an integer is equivalent to adding its additive inverse (opposite), converting all subtraction into addition.
Key Concepts
To subtract an integer, you add its opposite. For any integers $a$ and $b$: $$a b = a + ( b)$$.
Common Questions
How do you subtract integers by adding the opposite?
Change the subtraction to addition and change the sign of the number being subtracted. Then apply addition rules: a minus b equals a plus (negative b).
What is the additive inverse?
The additive inverse of a number is its opposite. The additive inverse of 7 is negative 7, and the additive inverse of negative 5 is 5. Any number plus its additive inverse equals 0.
What is an example of subtracting by adding the opposite?
To solve 3 minus (negative 4): rewrite as 3 plus 4 equals 7. To solve negative 2 minus 5: rewrite as negative 2 plus (negative 5) equals negative 7.
Why does subtracting equal adding the opposite?
Because subtraction and the additive inverse are defined to produce the same result. This rule allows you to apply addition rules consistently to all integer arithmetic.
What chapter covers integer subtraction in Illustrative Mathematics Grade 7?
Subtracting integers by adding the opposite is covered in Chapter 5: Rational Number Arithmetic in Illustrative Mathematics Grade 7.