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M.4 Complete addition and subtraction sentences with mixed numbers

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What does it mean to complete a number sentence?

To complete a number sentence means to find the missing number that makes the equation true. You use what you know about addition and subtraction to fill in the blank.

Examples:
  • ___ + 2 12 = 5 12
  • To find the missing number, subtract: 5 12 − 2 12 = 3
  • So, the completed sentence is: 3 + 2 12 = 5 12
Note

Use the relationship between addition and subtraction to find the missing value. If one part is missing in an addition sentence, use subtraction to find it—and if one part is missing in a subtraction sentence, use addition.

Adding mixed numbers to complete sentences

When you complete an addition sentence, add the whole numbers and fractions separately. If denominators are different, find a common denominator before adding.

Example:
  • 2 25 + ___ = 5 35
  • Subtract to find the missing addend: 5 35 − 2 25 = 3 15
  • So, 2 25 + 3 15 = 5 35
Note

You can check your work by adding the numbers again to see if your answer matches the total.

Completing sentences with unlike denominators

If the denominators are different, find the least common denominator before adding or subtracting. Then rewrite each fraction with that denominator.

Example:
  • ___ + 1 13 = 3 12
  • Rename 13 as 26 and 12 as 36
  • Now solve: ___ = 3 36 − 1 26 = 2 16
Note

Making denominators the same lets you compare and combine equal parts. This makes addition and subtraction fair and accurate.

Subtracting mixed numbers to complete sentences

When completing subtraction sentences, subtract the smaller number from the larger one. If the fractional part is not large enough, rename one whole as a fraction with the same denominator to help subtract.

Examples:
  • 6 23 − ___ = 3 13
  • Subtract to find the missing number: 6 23 − 3 13 = 3 13
  • So the missing number is 3 13.
  • Another example: ___ − 2 34 = 5 14
  • Add to find the missing number: 5 14 + 2 34 = 8
  • So, 8 − 2 34 = 5 14
Note

Use the opposite operation to check your work. If you used subtraction to find the missing number, add it back to the smaller number to see if it equals the larger number.

Checking your completed number sentences

After completing a number sentence, always verify your answer by doing the reverse operation. Your sentence is complete when both sides of the equation are equal.

Example:
  • ___ + 3 12 = 7
  • Subtract to find the missing number: 7 − 3 12 = 3 12
  • Check: 3 12 + 3 12 = 7 ✔
Note

Equations are like balance scales—both sides must show the same value. Always check that your completed sentence keeps both sides equal.