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The roles of the numbers
In 703 − 286 = 417, 703 is the minuend, 286 the subtrahend, and 417 the difference. Align places and start with ones. Order matters: subtraction is not commutative.
Regrouping preserves the total
If there are not enough ones, exchange one ten for ten ones. If there are no tens, first exchange one hundred for ten tens. The total stays the same; only its arrangement changes.
Do not simply subtract the smaller digit
In 52 − 28, do not calculate 8 − 2 merely because it is easier. Regroup one ten: 52 becomes 4 tens and 12 ones. Then 12 − 8 = 4 and 4 − 2 = 2, giving 24.
Worked examples
703 − 286 = 417
703 = 6 hundreds + 10 tens + 3 ones = 6 hundreds + 9 tens + 13 ones. Subtract: 13 − 6 = 7; 9 − 8 = 1; 6 − 2 = 4.
640 − 175 = 465
Regroup 640 as 5 hundreds, 13 tens, and 10 ones. The difference is 4 hundreds, 6 tens, and 5 ones. Check: 465 + 175 = 640.
Try it yourself
Your turn
Type the missing word, number, or sign. Spaces in large numbers are allowed. Try first, then open the explanation.
Explain how to calculate 600 − 248. State the regrouping, result, and check.
See an example answer
600 = 5 hundreds, 9 tens, and 10 ones. The difference is 352. Check: 352 + 248 = 600.
Check your knowledge
Choose one answer for each question. You can revise your answers and check again.
Answer key
- 415. Exchange one ten for ten ones.
- 424. Regroup 902 into 8 hundreds, 9 tens, and 12 ones.
- 62. 50 + 12 = 62.
- 465 + 175 = 640. The difference plus the subtrahend must recover the minuend.
- 499. The number immediately before 500 is 499.