L6 · Subtracting integers: a difference is a sum

Learning goal

“I can subtract any integer by rewriting the difference as a sum: a - b = a + (-b). Subtracting a negative means adding its opposite, and a difference can also tell me the distance between two numbers.”

Difference — the result of a subtraction. The difference in -2 - (-7) is 5.

Rewrite as a sum — changing a subtraction into the matching addition: a - b becomes a + (-b). The value does not change; only the form does.

Distance between two numbers — how far apart their positions are on the number line. Distance is never negative, and it equals the (positive) difference between them.

Worked example

3 - 5. Step 1: Rewrite the difference as a sum: subtracting 5 is the same journey as adding its inverse. 3 - 5 = 3 + (-5). Step 2: Use L5: different signs - magnitudes 3 and 5, the negative has more. 3 + (-5) = -2. Step 3: Check on the line: start at 3, subtracting a positive moves LEFT 5, landing on -2. Model both ways, side by side: line movement for 3 - 5, AND the counter mat where "subtract 5" is done by adding 5 negative counters (adding zero pairs keeps this legal - the rewrite in action). Subtraction is not a new operation. Every difference is a sum wearing a coat: a - b = a + (-b).

Check yourself — explain it

Why can 3 - 5 be rewritten as 3 + (-5)?

Paired problem — example still visible

-2 - 3. Rewrite, then solve: -2 + (-3) = -5

Faded completion — last step is yours

"5 - 8 = 5 + (___) = ___." -> -8; -3

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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