--- title: "Mixed numbers and improper fractions" description: "Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)" canonical: https://lightmysky.com/learn/mathematics/mixed-numbers-and-improper-fractions-mt_o_p-3tCxiM source: https://lightmysky.com/learn/mathematics/mixed-numbers-and-improper-fractions-mt_o_p-3tCxiM.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Mixed numbers and improper fractions Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5) Subject: Mathematics · Area: Fractions · Ages 9 to 10 Page: https://lightmysky.com/learn/mathematics/mixed-numbers-and-improper-fractions-mt_o_p-3tCxiM ## Ready when they can - Convert improper fractions to mixed numbers, identify their whole and fraction parts, and check that the fraction part is proper, including 11/4 = 2 3/4 - Count fractional parts in given wholes and convert mixed numbers to improper fractions, including 3 2/5 = 17/5 - Add fractions or mixed numbers with matching denominators and express the sum as an improper fraction, mixed number or whole number, including 6/5 + 4/5 = 10/5 = 2 ## Lesson: Mixed numbers and improper fractions An improper fraction has a numerator equal to or greater than its denominator. It names one whole or more. A mixed number has a whole number beside a proper fraction. The whole number counts complete wholes, and the fraction counts the extra part. *(drawing: Four quarters fill one whole: 4/4 = 1.)* **Example.** To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient counts wholes. Write the remainder over the same denominator. For 14/5, 2 × 5 = 10 and 3 × 5 = 15 is too much. There are 2 wholes and 4 fifths left: 2 4/5. The remainder must be smaller than the denominator. **Example.** To change a mixed number to an improper fraction, count every part in the same units. Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 1 2/7, the whole contains 7 sevenths. Add 2 more: 7 + 2 = 9. So 1 2/7 = 9/7. **Example.** When denominators match, add the numerators and keep the denominator. The parts keep their size. For 4/3 + 5/3, add 4 + 5 = 9 thirds. Group them in threes: 9/3 = 3. If parts remain after making wholes, write those parts over the same denominator. **Example.** To add mixed numbers with matching denominators, add their whole numbers and then their fraction parts. For 1 1/6 + 2 3/6, the wholes make 3 and the sixths make 4/6. The total is 3 4/6. If the fraction parts fill another whole, include it in the whole-number part. You can check a conversion by rebuilding the original numerator. Multiply the mixed number's whole part by its denominator, then add its fraction's numerator. Also check that its fraction part is proper. To find a missing whole part, remove the extra fraction's numerator first, then group the remaining parts into wholes. **Recap.** An improper fraction and a mixed number can name the same amount, so you can convert between them by dividing or by multiplying and adding. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Understanding fractions (age 9+)](https://lightmysky.com/learn/mathematics/understanding-fractions-age-9-mt_09sySPqM9Z) - [Whole numbers as fractions](https://lightmysky.com/learn/mathematics/whole-numbers-as-fractions-mt_AYzE1EAvI0) - [Fraction notation](https://lightmysky.com/learn/mathematics/fraction-notation-mt_vKcxX6iNOA) ## Opens up - [Adding fractions (unlike denominators)](https://lightmysky.com/learn/mathematics/adding-fractions-unlike-denominators-mt_14T5yPXUq_) - [Adding and subtracting mixed numbers](https://lightmysky.com/learn/mathematics/adding-and-subtracting-mixed-numbers-mt_70qDTI14td) - [Comparing fractions (age 10+)](https://lightmysky.com/learn/mathematics/comparing-fractions-age-10-mt_PL9VkDwXfh) - [Multiplying fractions](https://lightmysky.com/learn/mathematics/multiplying-fractions-mt_TgHxujL81r)