Other Ways to Add and Subtract — Part 2
4A · Chapter 2 · Lesson 4 · MATH-4A-C02-L04
Learning goal. Use equal adjustments, counting-up and inverse relationships for efficient subtraction.
Before you begin
Recall: 4A Ch1: million-range place value; Grade 3: column algorithms and comparison bars; Other Ways to Add and Subtract — Part 1. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Use compensation to add 525,356 and 28,503. What is the exact sum?
Show answer & reasoning
Increase 525,356 by 4 to a friendly multiple of 10, then subtract 4 from the sum to preserve the total.
Use compensation to add 631,200 and 183,544. What is the exact sum?
Show answer & reasoning
Increase 631,200 by 10 to a friendly multiple of 10, then subtract 10 from the sum to preserve the total.
Use compensation to add 644,834 and 159,481. What is the exact sum?
Show answer & reasoning
Increase 644,834 by 6 to a friendly multiple of 10, then subtract 6 from the sum to preserve the total.
Key vocabulary
- regroup
- exchange equal-value units
- compensation
- temporary adjustment corrected afterward
- sum
- result of addition
- difference
- result of subtraction
Understand the concept
A difference stays the same if you add the same amount to both numbers. For 6,002 − 998, add two to both and calculate 6,004 − 1,000 = 5,004. Counting upward from the smaller number is another valid strategy. The important question is why the adjustment preserves the difference.
Model it: two aligned number lines and a difference bar. 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 178,774 − 6,507 by adding 10 to both quantities first. What answer do you get?
Equal adjustment preserves the difference: (178,784) − (6,517) = 172,267.
Check your understanding 1
Calculate 707,804 − 208,043 by adding 50 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (707,854) − (208,093) = 499,761.
Worked example 2
Calculate 261,960 − 109,619 by adding 1000 to both quantities first. What answer do you get?
Equal adjustment preserves the difference: (262,960) − (110,619) = 152,341.
Check your understanding 2
Calculate 187,509 − 72,598 by adding 100 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (187,609) − (72,698) = 114,911.
Worked example 3
Calculate 649,364 − 213,247 by adding 10 to both quantities first. What answer do you get?
Equal adjustment preserves the difference: (649,374) − (213,257) = 436,117.
Check your understanding 3
Calculate 332,073 − 55,995 by adding 1000 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (333,073) − (56,995) = 276,078.
Guided practice
Calculate 199,413 − 61,206 by adding 100 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (199,513) − (61,306) = 138,207.
Calculate 719,458 − 127,100 by adding 1000 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (720,458) − (128,100) = 592,358.
Calculate 779,085 − 134,457 by adding 10 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (779,095) − (134,467) = 644,628.
Calculate 648,536 − 88,988 by adding 100 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (648,636) − (89,088) = 559,548.
Calculate 258,183 − 26,830 by adding 50 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (258,233) − (26,880) = 231,353.
Independent practice
Calculate 783,840 − 173,262 by adding 10 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (783,850) − (173,272) = 610,578.
Calculate 65,580 − 21,440 by adding 50 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (65,630) − (21,490) = 44,140.
Calculate 575,863 − 113,793 by adding 1000 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (576,863) − (114,793) = 462,070.
Calculate 332,668 − 98,504 by adding 50 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (332,718) − (98,554) = 234,164.
Calculate 651,504 − 134,076 by adding 10 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (651,514) − (134,086) = 517,428.
Calculate 666,418 − 10,341 by adding 10 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (666,428) − (10,351) = 656,077.
Calculate 313,351 − 24,998 by adding 1000 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (314,351) − (25,998) = 288,353.
Calculate 265,016 − 167,316 by adding 100 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (265,116) − (167,416) = 97,700.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Explain why 473 − 125 = 475 − 127. Find the common difference.
Show answer & reasoning
Adding two to both quantities preserves their difference: 348.
Calculate 179,091 − 98,352 by adding 50 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (179,141) − (98,402) = 80,739.
Exit check
Calculate 471,195 − 214,687 by adding 100 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (471,295) − (214,787) = 256,508.
Calculate 589,579 − 7,092 by adding 10 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (589,589) − (7,102) = 582,487.
Calculate 200,206 − 134,917 by adding 1000 to both quantities first. What answer do you get?
Show answer & reasoning
Equal adjustment preserves the difference: (201,206) − (135,917) = 65,289.