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Stage 4 of 20

Subtraction With Borrowing

Solve teen subtraction by decomposing through 10, counting up, and regrouping one ten as ten ones while checking every difference with addition.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Recognize subtraction facts that cross the boundary at 10
  • Decompose the subtrahend to subtract to ten and then below it
  • Use counting up as an equivalent difference strategy
  • Explain why regrouping preserves the original teen quantity

Understanding Subtraction With Borrowing

Teen subtraction becomes challenging when the amount removed exceeds the visible ones. In 13 − 8, the 3 ones cannot supply 8 ones. Regroup 13 as thirteen ones. The value stays constant; only its representation changes.

One mental route is to subtract through ten. Split 8 into 3 and 5 because 13 − 3 reaches 10; then 10 − 5 = 5. This is supported by the associative structure of subtraction in this context: removing a total of 8 can be done by removing its two parts successively.

A second route measures the gap by adding up. From 8 to 10 is 2, and from 10 to 13 is 3, so the complete distance is 5. The number line shows why this gives the same answer as taking away: both methods measure the interval between 8 and 13, only from different directions.

Stage 3 fact families remain the checking tool. If 13 − 8 = 5, then 8 + 5 = 13. Stage 2 make-ten reasoning also returns: 8 needs 2 to reach 10 and then 3 more to reach 13. Regrouping is therefore not an unrelated trick; it combines earlier addition, subtraction, and complement ideas.

Choose the method to fit the numbers. Subtract-through-ten is clear when the starting teen is easy to decompose. Counting up is compact when the endpoints are close. In both cases, record each jump mentally and add the partial distances rather than guessing from a memorized pattern.

Why This Skill Matters

Crossing backward through ten is the conceptual foundation for borrowing in larger numbers. Trading one ten for ten ones will later allow calculations such as 52 − 7 and 72 − 38 without changing the value of the minuend.

Teen differences also occur in elapsed scores, small change, and comparisons. Understanding the boundary at ten makes those situations easier to model and check.

Worked Examples: Think It Through

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Subtract through ten

13 − 8

  1. 1 I remove 3 first because 13 − 3 reaches 10.
  2. 2 Eight is 3 and 5, so I still need to remove 5.
  3. 3 Ten minus 5 leaves 5.

13 − 8 = 5

Your turn — try it on new numbers

14 − 8 = ?

Count up across ten

12 − 7

  1. 1 From 7 to 10 is a jump of 3.
  2. 2 From 10 to 12 is another 2.
  3. 3 The full gap is 3 + 2 = 5.

12 − 7 = 5

Your turn — try it on new numbers

14 − 7 = ?

Regroup one ten

15 − 9

  1. 1 I view 15 as ten ones and five more ones.
  2. 2 Removing 9 from the group of 10 leaves 1.
  3. 3 I combine that 1 with the untouched 5.

15 − 9 = 6

Your turn — try it on new numbers

13 − 8 = ?

Check by adding back

17 − 8

  1. 1 I count up: 8 to 10 is 2, then 10 to 17 is 7.
  2. 2 The distance is 2 + 7 = 9.
  3. 3 I verify that 8 + 9 = 17.

17 − 8 = 9

Your turn — try it on new numbers

15 − 6 = ?

Common Mistakes and How to Fix Them

Subtracting only from the ones digit

In 13 − 8, calculating 8 − 3 reverses the local digits and ignores the ten. Regroup the whole 13, then remove 8 or measure the gap.

Stopping at ten

Reaching 10 completes only the first part of a through-ten subtraction. Track how much of the subtrahend remains and remove that part too.

Adding partial gaps incorrectly

When counting from 8 to 13, the jumps are 2 and 3, not the endpoints 10 and 13. Add the distances 2 + 3 to obtain 5.

Subtraction With Borrowing in Everyday Life

A box begins with 14 markers and 9 are handed out. Remove 4 to reach the landmark of 10, then remove the remaining 5; five markers stay in the box. A quick addition check, 9 + 5 = 14, confirms the inventory.

For a temperature comparison from 8 degrees to 16 degrees, count up 2 degrees to 10 and 6 more to 16. The combined gap of 8 uses the same across-ten structure without a take-away story.

Pro Tips

  • • Circle ten mentally as the bridge between a teen number and a single digit.
  • • Split the amount being removed, never change its total.
  • • Use count-up when the subtrahend and minuend are close together.
  • • Finish with an addition equation that reconstructs the starting teen.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 11 − 6 = ?
  2. 2. 12 − 8 = ?
  3. 3. 13 − 7 = ?
  4. 4. 14 − 9 = ?
  5. 5. 15 − 8 = ?
  6. 6. 16 − 9 = ?
  7. 7. 17 − 8 = ?
  8. 8. 12 − 5 = ?
  9. 9. 13 − 9 = ?
  10. 10. 14 − 6 = ?
  11. 11. 15 − 7 = ?
  12. 12. 16 − 8 = ?
  13. 13. 17 − 9 = ?
  14. 14. 11 − 4 = ?
  15. 15. 12 − 7 = ?
  16. 16. 13 − 5 = ?
  17. 17. 14 − 8 = ?
  18. 18. 15 − 9 = ?

Drill Stage 4 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses subtraction from teen numbers that needs regrouping. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

16 − 9 = ?

Stage 4 Questions

Why is regrouping sometimes called borrowing?

The traditional word describes taking one ten from the tens place, but regrouping is more precise: that ten is exchanged for ten ones of equal value.

Is counting up really subtraction?

Yes. It finds the distance between the subtrahend and minuend, which is the same difference represented by subtraction.

How do I know whether a fact crosses ten?

If removing the subtrahend from the ones beyond ten requires passing 10 to reach a single-digit answer, an across-ten strategy is useful.