Grade 2 · Operations · MAT-02-OPS-006
Subtract Two-Digit Numbers with Regrouping
Subtract two-digit numbers when regrouping is required.
Learning objectives
What you should be able to do
- Subtract two-digit numbers when regrouping is required.
- Regroup one ten as ten ones using models and symbols.
- Explain why regrouping preserves the number's total value.
Prerequisite check
Make sure the foundation is ready.
Checks both equivalence and subtraction foundations.
Learn
Build the idea from meaning, not memorization.
Regroup when there are not enough ones
In 52−27, 2 ones cannot directly remove 7 ones. Trade one of the 5 tens for 10 ones. The number is still 52, now represented as 4 tens and 12 ones.
Subtract after the trade
From 12 ones subtract 7 to get 5 ones. From the remaining 4 tens subtract 2 tens to get 2 tens. The difference is 25.
Regrouping changes representation, not value
5 tens 2 ones and 4 tens 12 ones both equal 52. The trade makes subtraction possible while preserving the original quantity.
Check with addition
If 52−27=25, then 25+27 should equal 52. The inverse operation is a strong error check.
Interactive math lab
Change it. See what stays true.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- trade ten
- remove ones
- remove tens
- inverse check
Worked examples
Twenty different ways to see the concept work.
52−27
25Regroup52 as4T12O.
61−36
25Regroup61 as5T11O.
73−48
25Regroup73 as6T13O.
84−59
25Regroup84 as7T14O.
92−67
25Regroup92 as8T12O.
40−18
22Regroup40 as3T10O.
50−26
244T10O−2T6O.
63−29
345T13O−2T9O.
71−45
266T11O−4T5O.
82−57
257T12O−5T7O.
90−38
528T10O−3T8O.
54−19
354T14O−1T9O.
62−28
345T12O−2T8O.
75−39
366T15O−3T9O.
81−46
357T11O−4T6O.
43−18
253T13O−1T8O.
70−25
456T10O−2T5O.
64−37
275T14O−3T7O.
Explain 52−27 regrouping.
52=4T12O;12−7=5;4T−2T=2T.Difference25.
Check 52−27=25.
25+27=52Inverse confirms result.
Practice
Guided practice with hints
0162−37
Hint: Regroup one ten.
Answer: 25
0271−46
Hint: 6T11O.
Answer: 25
0380−35
Hint: 7T10O.
Answer: 45
0453−28
Hint: 4T13O.
Answer: 25
0594−58
Hint: 8T14O.
Answer: 36
06Why doesn't regrouping change 52?
Hint: 1 ten equals10 ones.
Answer: 4T12O still equals52.
Practice
Independent practice
0164−29
Answer: 35
0272−48
Answer: 24
0381−56
Answer: 25
0450−27
Answer: 23
0593−58
Answer: 35
0670−36
Answer: 34
0762−19
Answer: 43
0884−47
Answer: 37
Common mistakes
Learn to catch the error, not just the answer.
A regroup is a trade: remove one ten and add ten ones.
Keep operand order fixed; regroup when needed.
After trading one ten, use the new tens count.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Make change or compare quantities when a tens trade is needed.
- Use base-ten blocks to physically trade one ten-rod for ten unit cubes.
Challenge problems
Why is 52 still 52 after becoming4T12O?
40+12=52, same total.
Find a subtraction requiring regrouping with difference30.
Example 65−35 does not regroup; a valid regrouping example is 64−34? no. Example 72−42 no. Use 71−41 no. Example 63−33 no. One valid is 58−28 no. Use 62−32 no. Better: 71−41 no. A valid answer is 82−52 no. Need ones top<bottom: 74−44 no. Difference30 with same ones impossible when no borrow? Use 53−23 no. For difference30 and borrow, e.g. 61−31 no. Borrow changes tens by1 but ones difference adds10; equation can work if bottom ones > top ones and tens difference adjusted: 52−22 no. Actually any exact 30 means same ones modulo10, so no borrow. Thus impossible for two-digit integers with same integer difference30 and one borrow? Could have 40−10 no. So answer: impossible if both are whole two-digit numbers and standard one-step borrow because exact multiple-of-10 difference implies equal ones digits.
Explain why 80−37 becomes7T10O−3T7O.
One ten is traded for10 ones.
Check 64−29 using addition.
35+29=64.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Regroup & Remove
Trade tens for ones only when needed, then subtract accurately.
Practice
Mastery check
0162−37
Answer: 25
0281−46
Answer: 35
0370−28
Answer: 42
0453−19
Answer: 34
05Why trade1 ten?
Answer: To create10 more ones when top ones are insufficient.
06Does regrouping change value?
Answer: No
07Check52−27=25.
Answer: 25+27=52
08Explain80−35.
Answer: 80=7T10O;10−5=5;7T−3T=4T;45.
Terminology
Words to know
- regroup
- Exchange equivalent place-value units.
- trade
- Replace one place-value unit with an equal value of smaller units.
- difference
- The result of subtraction.
- inverse
- An operation that reverses another.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.NBT.B.5
Subtraction within 100 using place-value strategies.