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Subtract across zeros

This understanding involves subtracting multi-digit whole numbers when one or more zero-valued place positions require regrouping across adjacent places, such as in 5,000−2,3475{,}000-2{,}347. The learner interprets regrouping as decomposing one unit of a higher place into ten units of the next place, preserves place value while recording the result, and distinguishes placeholder zeros from quantities available for subtraction; decimal and negative-number cases are not included.

Detailed Explanation: Subtract across zeros

When subtracting across zeros, regroup from the first nonzero place to the left. Each regrouping changes 1 unit into 10 units of the next smaller place.

Example:

5,000−2,3475{,}000-2{,}347
  1. Start in the ones place. There are 00 ones, so we cannot subtract 77 ones. The tens and hundreds places are also 00, so regroup from the thousands place.
  2. Take 11 thousand from 55 thousands. This leaves 44 thousands and makes (10)(10) hundreds.
  3. Regroup 11 hundred into (10)(10) tens. Now there are 99 hundreds and (10)(10) tens.
  4. Regroup 11 ten into (10)(10) ones. Now there are 99 tens and (10)(10) ones.

The number is now ready to subtract by place value:

499102347\begin{array}{rrrr} 4 & 9 & 9 & 10\\ 2 & 3 & 4 & 7\\ \hline \end{array}

Subtract from right to left:

  • Ones: (10−7=3)(10-7=3)
  • Tens: (9−4=5)(9-4=5)
  • Hundreds: (9−3=6)(9-3=6)
  • Thousands: (4−2=2)(4-2=2)

Therefore,

5,000−2,347=2,6535{,}000-2{,}347=\boxed{2{,}653}

The zeros were placeholders, so they did not provide any units to subtract until we regrouped from a larger place.

Learn by doing: Subtract across zeros

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    Subtraction - Whole Number - Across Zeros

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