A mixed number like 2 3/4 has whole ones and a fraction. Each whole is made of the same parts: 1 whole = 4 quarters. So 2 3/4 is 2 × 4 + 3 = 11 quarters, written 11/4. To go the other way, divide: 17/5 is 17 ÷ 5 = 3 remainder 2, so 3 wholes and 2 fifths, written 3 2/5. The fraction part of a mixed number is always less than 1, and the denominator never changes.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- mixed number
- a whole number and a fraction together, like 3 2/5
- improper fraction
- a fraction whose numerator is bigger than its denominator
- simplest form
- a fraction whose top and bottom have no common factor bigger than 1
Worked examples
Write 2 3/4 as an improper fraction.
- 1.2 wholes are 2 × 4 = 8 quarters.
- 2.8 + 3 = 11 quarters: 11/4.
= 11/4
Write 17/5 as a mixed number.
- 1.17 ÷ 5 = 3 remainder 2.
- 2.3 wholes and 2 fifths: 3 2/5.
= 3 2/5
Write 14/4 as a mixed number in simplest form.
- 1.14 ÷ 4 = 3 remainder 2, so 3 2/4.
- 2.2/4 simplifies to 1/2.
= 3 1/2
For parents
Method: Wholes are groups of parts
What to say: How many parts are in one whole? How many whole ones can you make?
Common mistakes:
- Adds the whole number to the numerator (2 3/4 → 5/4).
- Multiplies the whole number by the denominator but forgets to add the numerator.
- Multiplies the whole number by the numerator and adds the denominator (2 3/4 → 10/4).
- Writes the remainder as the whole number and the quotient as the numerator.
- Puts the remainder over the original numerator instead of the denominator.
- Takes out one whole too few, leaving an improper fraction part (17/5 → 2 7/5).
- Gives only the whole-number part and drops the remainder.
- Converts correctly but leaves the fraction part unsimplified when simplest form is asked for.