Subtraction
4A · Chapter 2 · Lesson 2 · MATH-4A-C02-L02
Learning goal. Solve differences with multiple exchanges, including through zeros, and check by addition.
Before you begin
Recall: 4A Ch1: million-range place value; Grade 3: column algorithms and comparison bars; Addition. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Calculate 327,246 + 156,808.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 112,987 + 175,875.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 31,801 + 113,309.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Key vocabulary
- regroup
- exchange equal-value units
- compensation
- temporary adjustment corrected afterward
- sum
- result of addition
- difference
- result of subtraction
Understand the concept
Subtraction removes equal-valued units from a whole. If there are too few ones, rename one ten as ten ones; the quantity does not change. Across zeros, keep exchanging until an available higher-place unit can be renamed. Verify a difference by adding it back to the subtracted amount.
Model it: exchange chart and inverse addition. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 509,925 − 53,724.
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 456,201 + 53,724 = 509,925.
Check your understanding 1
Calculate 444,468 − 5,917.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 438,551 + 5,917 = 444,468.
Worked example 2
Calculate 457,936 − 53,633.
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 404,303 + 53,633 = 457,936.
Check your understanding 2
Calculate 291,630 − 199,606.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 92,024 + 199,606 = 291,630.
Worked example 3
Calculate 791,896 − 114,796.
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 677,100 + 114,796 = 791,896.
Check your understanding 3
Calculate 509,011 − 153,138.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 355,873 + 153,138 = 509,011.
Guided practice
Calculate 715,988 − 204,320.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 511,668 + 204,320 = 715,988.
Calculate 357,507 − 105,088.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 252,419 + 105,088 = 357,507.
Calculate 816,028 − 136,427.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 679,601 + 136,427 = 816,028.
Calculate 574,921 − 21,484.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 553,437 + 21,484 = 574,921.
Calculate 843,992 − 217,370.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 626,622 + 217,370 = 843,992.
Independent practice
Calculate 810,165 − 154,237.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 655,928 + 154,237 = 810,165.
Calculate 467,538 − 81,451.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 386,087 + 81,451 = 467,538.
Calculate 444,520 − 215,197.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 229,323 + 215,197 = 444,520.
Calculate 354,250 − 26,570.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 327,680 + 26,570 = 354,250.
Calculate 589,786 − 22,448.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 567,338 + 22,448 = 589,786.
Calculate 677,217 − 31,115.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 646,102 + 31,115 = 677,217.
Calculate 282,295 − 161,814.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 120,481 + 161,814 = 282,295.
Calculate 398,791 − 36,366.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 362,425 + 36,366 = 398,791.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Find 43,002 − 9 and explain how regrouping across zeros works.
Show answer & reasoning
Exchange from higher places so the ones column contains enough ones. The difference is 42,993.
Calculate 635,213 − 34,048.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 601,165 + 34,048 = 635,213.
Exit check
Calculate 652,600 − 162,202.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 490,398 + 162,202 = 652,600.
Calculate 831,681 − 183,054.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 648,627 + 183,054 = 831,681.
Calculate 388,227 − 109,334.
Show answer & reasoning
Subtract like place values, exchanging one higher unit for ten lower units when necessary. Check: 278,893 + 109,334 = 388,227.