Completing the Ten, at Any Scale — and Compensation
97 + 46 looks nothing like 7 + 5. It isn't. The gap-to-the-friendly-number
trick from the last lesson doesn't care how many digits are involved — it just
needs a friendly number nearby. For 97, that's not ten. It's a hundred.
The same trick, aimed further
Split 46 the same way you split 6 last time: the piece that fills the gap,
and whatever's left.
97 + 46
= 97 + 3 + 43 (3 fills the gap to 100, 43 is what's left of 46)
= 100 + 43 (97 + 3 is exactly 100)
= 143See it on the same diagram as before, just re-aimed:
The first jump completes the hundred. The second jump adds what's left of 46. Same two-hop idea as before, just aimed at a bigger friendly number.
When splitting isn't the easy part
Completing the ten works best when the first number is close to a friendly
one. Sometimes it's the second number that's close instead — 58 + 39 has
nothing convenient about 58, but 39 is one short of 40. For those,
there's a second move: round the awkward number up to the friendly one,
add the easy sum, then take back the extra you added.
Here's what that looks like for 58 + 39:
Round 39 up to 40 and land on 98 — one jump too far. Step back the 1 you added extra, and you're at 97, exactly 58 + 39.
This is the one place people trip on compensation: the amount you take back has to match exactly how much you rounded up by — no more, no less. Round up by 1, correct by 1. Round up by 7, correct by 7.
The same move works past two digits. 156 + 89: 89 is 1 short of 90, so
round up, add the easy sum, then correct back:
156 + 90 = 246 is the easy sum. Step back the 1 you added extra, and you're at 245 — 156 + 89 exactly.
Picking which piece to round
Completing the ten (split the second number) and compensation (round it up
instead) are the same idea from two directions. Pick whichever number sits
closer to a friendly one, and work from there — the smaller the gap, the
shorter the detour. For 58 + 39, compare both gaps side by side:
58's gap to the nearest ten is 2.
39's gap to the nearest ten is only 1 — smaller than 58's.
🎯 Your turn
Pick a number close to a friendly one — a ten, a hundred, whatever fits — and add something to it two ways: split the second number to complete the friendly one, and separately round up and correct back. Confirm both land on the same total before you move on to the explain exercise below.