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J.3 Complete addition and subtraction sentences

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Understanding addition sentences

Addition sentences show how two or more numbers combine to make a total sum. When working with three-digit numbers, we add ones to ones, tens to tens, and hundreds to hundreds.

Example with regrouping:

Let's solve 148 + 276 step by step:

148
+ 276
424
  • Start with ones place: 8 + 6 = 14. Write 4, carry 1 to tens place.
  • Tens place: 4 + 7 + 1 (carried) = 12. Write 2, carry 1 to hundreds place.
  • Hundreds place: 1 + 2 + 1 (carried) = 4.
  • The complete sentence: 148 + 276 = 424
Note

Always begin adding from the ones place (rightmost digit) and move left. Regrouping (carrying) happens when a column's sum is 10 or greater.

Understanding subtraction sentences

Subtraction sentences show how much remains when we take one number away from another. With three-digit numbers, we subtract ones from ones, tens from tens, and hundreds from hundreds.

Example with regrouping:

Let's solve 532 - 187 step by step:

532
- 187
345
  • Start with ones place: 2 - 7 (can't do). Regroup from tens: 2 becomes 12, tens place reduces from 3 to 2.
  • Ones: 12 - 7 = 5
  • Tens place: 2 - 8 (can't do). Regroup from hundreds: 2 becomes 12, hundreds place reduces from 5 to 4.
  • Tens: 12 - 8 = 4
  • Hundreds place: 4 - 1 = 3
  • The complete sentence: 532 - 187 = 345
Note

Always begin subtracting from the ones place. When a digit in the top number is smaller than the digit below it, regroup from the next place to the left.

Finding missing numbers in sentences

Sometimes addition and subtraction sentences have missing numbers. To find them, think about the relationship between the numbers and work backward from the answer.

Missing addend example:

Find the missing number: 256 + ? = 419

419
- 256
163

Since 256 + ? = 419, we subtract 256 from 419 to find the missing number: 419 - 256 = 163

Missing subtrahend example:

Find the missing number: 504 - ? = 329

504
- 329
175

Since 504 - ? = 329, we subtract 329 from 504 to find the missing number: 504 - 329 = 175

Note

Addition and subtraction are inverse operations. If you know the total and one part, subtract to find the missing part. If you know the difference and one number, either add or subtract to find the missing number.

Solving word problems with complete sentences

Real-world problems often require setting up and solving complete addition or subtraction sentences. Read carefully to determine whether to add or subtract.

Addition word problem:

Sarah collected 347 shells on Monday and 285 shells on Tuesday. How many shells did she collect in total?

347
+ 285
632

Complete sentence: 347 + 285 = 632 shells

Subtraction word problem:

The library had 713 books. After a book sale, 468 books remained. How many books were sold?

713
- 468
245

Complete sentence: 713 - 468 = 245 books sold

Note

Key words often indicate the operation: "total," "altogether," and "combined" suggest addition. "How many more," "difference," and "remain" suggest subtraction.

Checking your work

Good mathematicians always check their work. For addition, check by subtracting. For subtraction, check by adding.

Checking addition:

If 169 + 278 = 447, check by subtracting:

447
- 169
278

Since 447 - 169 equals 278 (our original addend), our addition is correct.

Checking subtraction:

If 620 - 354 = 266, check by adding:

266
+ 354
620

Since 266 + 354 equals 620 (our original number), our subtraction is correct.

Note

Checking your work helps catch mistakes and builds confidence in your answers. Always take a moment to verify your calculations.

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