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Stage 7 of 20

Two-Digit Plus Single (No Carry)

Learn no-carry addition through place-value reasoning, mental partitioning, clear justifications, worked examples, and carefully graded practice.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Partition any two-digit number into tens and ones before adding
  • Recognize when a one-digit addend will not create a new ten
  • Add to the ones while preserving the value of the tens
  • Justify and check a result with subtraction or an estimate

Why This Matters

Keeping place values separate makes larger calculations manageable. The same partitioning supports money totals, measurement changes, estimation, and later column addition.

Understanding Two-Digit Plus Single (No Carry)

A two-digit number is built from tens and ones. In 43, the 4 means four tens, or 40, while the 3 means three ones. Therefore 43 + 5 can be rewritten as 40 + 3 + 5. Combining the ones gives 8, so the total is 40 + 8 = 48. The tens do not change because no new group of ten has been made.

Before calculating, inspect the ones. If their sum is 9 or less, the problem belongs to this stage. For 62 + 7, the test is 2 + 7 = 9. It is safe to hold 60 steady and combine only 2 and 7. This small prediction prevents accidental carrying and gives a reason for every digit in 69.

You can justify the method with the associative property: (60 + 2) + 7 equals 60 + (2 + 7). The grouping changes, but the quantities do not. A number line gives the same conclusion: seven one-unit jumps from 62 land on 69 without crossing 70. Different representations agreeing is strong evidence that the answer is correct.

Stage 6 used doubles and near-doubles to make one-digit facts efficient. Those facts now work inside a place-value structure: in 54 + 5, the ones fact 4 + 5 = 9 can be seen as one more than 4 + 4 = 8. This stage prepares for Stage 8, where the same ones reasoning sometimes creates a complete new ten.

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.

Hold the tens steady

32 + 6

  1. 1 Partition 32 into 30 + 2.
  2. 2 Combine the ones: 2 + 6 = 8.
  3. 3 Rejoin the parts: 30 + 8 = 38.

32 + 6 = 38

Your turn — try it on new numbers

51 + 3 = ?

Add to a zero

70 + 9

  1. 1 Read 70 as seven tens and zero ones.
  2. 2 Add nine ones: 0 + 9 = 9.
  3. 3 Keep the seven tens to make 79.

70 + 9 = 79

Your turn — try it on new numbers

24 + 1 = ?

Use a near-double fact

54 + 5

  1. 1 Protect the 50 and focus on 4 + 5.
  2. 2 Use 4 + 4 = 8, then add 1 to get 9.
  3. 3 Combine 50 and 9.

54 + 5 = 59

Your turn — try it on new numbers

31 + 7 = ?

Check by reversing

81 + 7

  1. 1 Add the ones: 1 + 7 = 8.
  2. 2 Keep the 80, giving 88.
  3. 3 Check that 88 − 7 returns 81.

81 + 7 = 88

Your turn — try it on new numbers

72 + 5 = ?

Common Mistakes and How to Fix Them

Adding to the tens digit

Turning 42 + 5 into 92 treats five ones as five tens. Self-correct by expanding 42 as 40 + 2 and attaching the 5 only to the ones.

Joining digits instead of values

Writing 425 does not represent addition. Say “forty-two plus five,” calculate 2 + 5, and rebuild 40 + 7.

Using no-carry reasoning past nine

For 26 + 7, 6 + 7 is 13, so this method cannot leave the tens unchanged. Check the ones sum first and move to regrouping when it reaches 10.

Two-Digit Plus Single (No Carry) in Everyday Life

A library cart holds 53 books and receives 6 more. The 50 books remain as five full groups of ten; 3 + 6 makes 9 loose books, so the cart now holds 59. This exact structure appears when adding a few items to an existing stock.

Pro Tips

  • • Whisper the partition: “forty and three” before solving 43 + 4.
  • • Predict whether the next ten will be crossed by checking the ones first.
  • • Use a quick subtraction check when an answer feels uncertain.
  • • Picture bundled tens that cannot be opened during a no-carry problem.

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. 24 + 3 = ?
  2. 2. 51 + 6 = ?
  3. 3. 72 + 5 = ?
  4. 4. 40 + 8 = ?
  5. 5. 33 + 4 = ?
  6. 6. 61 + 7 = ?
  7. 7. 85 + 2 = ?
  8. 8. 12 + 6 = ?
  9. 9. 46 + 3 = ?
  10. 10. 90 + 9 = ?
  11. 11. 23 + 5 = ?
  12. 12. 74 + 4 = ?
  13. 13. 31 + 8 = ?
  14. 14. 56 + 2 = ?
  15. 15. 82 + 6 = ?
  16. 16. 15 + 4 = ?
  17. 17. 63 + 3 = ?
  18. 18. 70 + 7 = ?

Drill Stage 7 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses two-digit plus a single digit without carrying. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

25 + 3 = ?

Stage 7 Questions

How can I tell that no carrying is needed?

Add only the starting ones digit and the one-digit addend. If that total is below 10, no new ten is formed.

Why is the tens digit unchanged?

Only ones are added, and fewer than ten combined ones cannot be exchanged for an additional ten.

Can I count on instead of partitioning?

Yes. Counting on verifies the result, but partitioning makes the place-value reason visible and scales better to larger numbers.