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Mixed Numbers and Fraction Word Problems

A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.

A mixed number has a whole-number part and a fraction part. To operate with mixed numbers, you can convert to improper fractions or combine whole numbers and fraction parts separately. Context helps decide whether an improper fraction or mixed number is clearer. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Lumber lengths, baking ingredients, and pace times are usually written as mixed numbers. Converting between mixed and improper forms is what keeps each calculation step clean.

Worked example

Problem. Compute 1 2/3 + 2 1/6.

  1. Add whole numbers: 1 + 2 = 3.
  2. Add fractions: 2/3 + 1/6 = 4/6 + 1/6 = 5/6.
  3. The sum is 3 5/6.
  4. Connect the calculation back to Mixed Numbers and Fraction Word Problems so the method, not just the arithmetic, is clear.

Answer: 3 5/6

Practice problems

1. Convert 2 1/3 to an improper fraction.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Convert 2 1/3 to an improper fraction.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Multiply 2 x 3 = 6.
  4. Add the numerator: 6 + 1 = 7.
  5. Keep the denominator 3.
  6. Check the result by substituting or estimating: the response should match 7/3 and make sense in the original problem.

Answer: 7/3

2. Convert 9/4 to a mixed number.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Convert 9/4 to a mixed number.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 9 divided by 4 is 2 remainder 1.
  4. The mixed number is 2 1/4.
  5. Check the result by substituting or estimating: the response should match 2 1/4 and make sense in the original problem.

Answer: 2 1/4

3. Compute 1 1/2 + 2 1/2.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 1 1/2 + 2 1/2.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Add the whole numbers: 1 + 2 = 3.
  4. Add the fractions: 1/2 + 1/2 = 1.
  5. 3 + 1 = 4.
  6. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

4. Compute 3 1/4 + 1 1/2.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 3 1/4 + 1 1/2.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Rewrite 1/2 as 2/4.
  4. Add fractions: 1/4 + 2/4 = 3/4.
  5. Add wholes: 3 + 1 = 4.
  6. Check the result by substituting or estimating: the response should match 4 3/4 and make sense in the original problem.

Answer: 4 3/4

5. Compute 5 2/3 - 2 1/3.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 5 2/3 - 2 1/3.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Subtract whole numbers: 5 - 2 = 3.
  4. Subtract fractions: 2/3 - 1/3 = 1/3.
  5. Check the result by substituting or estimating: the response should match 3 1/3 and make sense in the original problem.

Answer: 3 1/3

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