Unbundling in subtraction
Unbundle tens and hundreds to subtract, including across zero, while preserving the starting amount.
Begin with the activity ↓To subtract 18 from 42, there are only two ones.
Exchange a ten for ten ones. Tens decrease by one and ones increase by ten, but the total stays the same.
42 consists of four tens and two ones. To remove 18 pencils, we need one ten and eight ones. Two loose ones are not enough, so open a ten-bundle.
There are now three tens and twelve ones: 30+12 is still 42. Remove eight ones, leaving four, and one ten, leaving two tens. The remaining amount is 24.
Subtracting the smaller digit from the larger in each column is a different calculation. Replacing the ones calculation with 8−2 reverses the story. Regroup the starting amount instead.
In 302−178, there are no tens to open. First exchange a hundred for ten tens: two hundreds, ten tens and two ones. Then open one ten: two hundreds, nine tens and twelve ones. The total is 302 throughout.
Remove one hundred, seven tens and eight ones to leave one hundred, two tens and four ones: 124. Check 124+178=302. What was removed and what remains combine to restore the original amount.
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If the tens place is zero
You do not borrow from zero. Exchange a hundred for ten tens first, then open one of those tens. Draw the two exchanges separately.
Now change it yourself
Unbundle until enough ones and tens are available, then subtract. For 302−178, begin by opening a hundred.
To remove: 0 hundreds, 1 tens and 8 ones
Hundreds 0
Tens 4
Ones 2
0×100 + 4×10 + 2 = 42
The differences here are nonnegative whole numbers. Leaving the original bundle after unpacking would count the same amount twice.
Try with paper and objects
Use paper place-value cards, replacing a hundred by ten tens and a ten by ten ones.
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44 · Unbundle as six tens and ten ones; subtract to leave four tens and four ones.
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Split a two-digit number into tens and ones, multiply both parts and recombine.