Fractions · lesson 17 of 24 · free

Mixed numbers and improper fractions — Fractions for kids

2 3/4 (two and three quarters) is a mixed number: 2 wholes and 3/4 more. As quarters, 2 wholes are 8 quarters, plus 3 is 11 quarters — the improper fraction 11/4, where the top is bigger than the bottom.

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The method

Multiply and add — “whole × bottom + top gives the improper fraction; divide to go back”

  1. Mixed → improper: whole × bottom + top; keep the bottom.
  2. Improper → mixed: divide top by bottom; the answer is the whole number and the remainder is the new top.
  3. The bottom number never changes.

Use it for: Adding, subtracting, multiplying and dividing mixed numbers (Class 5–7), and recipes like 2 1/2 cups.

🧮 Check your own sums with the free Fraction calculator — it shows the working.

Worked example: Write 2 3/4 as an improper fraction. → 11/4

  1. Multiply the whole number by the bottom: 2 × 4 = 8.
  2. Add the top: 8 + 3 = 11. The bottom stays 4.

Check: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4 ✓

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✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 17 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Mixed and Improper Fractions Worksheet

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