Subtracting Integers - Add the Opposite

Pre-Algebra · Axiom Academy

LESSON Subtracting Integers: Add the Opposite Why every subtraction is secretly an addition — turn a - b into a + (-b) and the signs sort themselves out. Subtraction and addition are two sides of the same coin. Taking b away from a gives the same result as adding the opposite of b . The minus sign becomes a plus sign , and the number that follows it flips to its opposite. "To subtract, add the opposite." Here's the case that looks strange: 8 - (-3) . Apply the rule. The opposite of -3 is +3 , so subtracting -3 turns into adding +3 . The watch the two minus signs — the subtraction and the negative — cancel each other into a single plus. On a number line, adding moves right and subtracting moves left . So what does subtracting a negative do? Rewrite it first: 8 - (-3) = 8 + 3 . Now it's an addition, which means we move right — the opposite of what plain subtraction would do. Start at 8 . Subtracting -3 means "add the opposite of -3 ," and the opposite of -3 is +3 . So jump 3 units to the right , landing on 11 . No matter what signs are involved, the move is identical: rewrite the subtraction as adding the opposite , then add. Here are all four sign combinations — watch each one convert. You've seen why subtracting is just adding the opposite — and why subtracting a negative makes a number grow. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.