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M.3 Add and subtract mixed numbers: word problems

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What are mixed numbers?

Mixed numbers are numbers that include both a whole number and a fraction. For example, 214 means “2 wholes and one-fourth.”

Examples:
  • 312 = 3 + 12
  • 134 = 1 + 34
Note

Mixed numbers can be changed to improper fractions to make addition or subtraction easier.

How to add mixed numbers

To add mixed numbers, add the whole numbers first, then the fractions. If the denominators are different, find a common denominator before adding the fractions.

Example:
  • 213 + 123
  • Add whole numbers: 2 + 1 = 3
  • Add fractions: 13 + 23 = 33 = 1
  • Total: 3 + 1 = 4
  • Answer: 4
Note

If the fraction part adds up to one or more wholes, regroup it into the whole number part.

How to subtract mixed numbers

To subtract mixed numbers, subtract the whole numbers and fractions separately. If the fraction in the first number is smaller, you may need to borrow 1 from the whole number.

Example:
  • 418 − 238
  • The fraction 18 is smaller than 38, so borrow 1 from 4.
  • 4 becomes 3, and add 1 whole (or 88) to the fraction part.
  • Now it’s 398 − 238 = 168
  • Simplify: 134
Note

Always check whether you need to borrow when subtracting fractions with the same or different denominators.

Word problems with mixed numbers

Word problems help you understand when and how to add or subtract mixed numbers in real-life situations. Read carefully to decide which operation to use.

Example 1: Adding

Emma walked 212 miles on Monday and 334 miles on Tuesday. How far did she walk in all?

  • 212 + 334 = 614
Example 2: Subtracting

Jack baked 525 pans of brownies. He sold 345 pans. How many pans does he have left?

  • 525 − 345 = 135
Note

Look for clue words: “in all” or “total” often mean add; “left” or “remain” often mean subtract.

Tips for solving mixed number problems

Use these steps to stay organized when working with mixed number problems:

Steps:
  • 1. Read the problem carefully and decide whether to add or subtract.
  • 2. Write the mixed numbers vertically, aligning whole numbers and fractions.
  • 3. Find a common denominator if needed.
  • 4. Add or subtract fractions and then whole numbers.
  • 5. Simplify your final answer.
Note

Always simplify your fractions and check your work with estimation to make sure your answer makes sense.