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Mixed Numbers and Improper fractions
Lesson: Mixed Numbers & Improper Fractions
Year 7 — LearnPress-ready HTML lesson. Clear explanations, worked examples and practice following the UK curriculum.
1. Definitions
Mixed number
A mixed number combines a whole number and a fraction. Example: 2 1/3 means 2 wholes and a third.
Improper fraction
An improper fraction has a numerator larger than or equal to the denominator. Example: 7/3.
2. Convert mixed number → improper fraction
Multiply the whole number by the denominator, add the numerator, write the result over the denominator.
Example: Convert 2 1/3 into an improper fraction.
3 × 2 = 6; 6 + 1 = 7 → 7/3
3. Convert improper fraction → mixed number
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator.
Example: Convert 11/4 into a mixed number.
11 ÷ 4 = 2 remainder 3 → 2 3/4
4. Why convert? (When to use each form)
- Use improper fractions to add, subtract, multiply or divide fractions easily.
- Use mixed numbers when you want a clearer, easier-to-read answer (for example, in measurements or recipes).
5. Worked examples
a) Add 1 1/2 + 2 2/3.
Convert: 1 1/2 = 3/2, 2 2/3 = 8/3.
LCM of 2 and 3 is 6 → 3/2 = 9/6, 8/3 = 16/6
Add: 9/6 + 16/6 = 25/6 = 4 1/6.
b) Subtract 3 1/4 - 1 2/5.
Convert: 3 1/4 = 13/4, 1 2/5 = 7/5.
LCM of 4 and 5 is 20 → 13/4 = 65/20, 7/5 = 28/20
Subtract: 65/20 - 28/20 = 37/20 = 1 17/20.
6. Common mistakes to avoid
- Forgetting to convert mixed numbers to improper fractions before calculation.
- Forgetting to find a common denominator when adding/subtracting.
- Leaving answers as improper fractions when a mixed number is clearer.
7. Practice
- Convert
4 2/5to an improper fraction. - Convert
27/8to a mixed number. - Calculate
2 3/7 + 1 5/14. - Calculate
5 1/6 - 2 2/3. - Write
9/4as a mixed number and then convert back to check.
Answers (teacher)
4 2/5 = (4×5+2)/5 = 22/527 ÷ 8 = 3 remainder 3 → 3 3/8- Convert:
2 3/7 = 17/7,1 5/14 = 19/14, LCM 14 →34/14 + 19/14 = 53/14 = 3 11/14 - Convert:
5 1/6 = 31/6,2 2/3 = 8/3 = 16/6, subtract →31/6 - 16/6 = 15/6 = 2 3/6 = 2 1/2 9/4 = 2 1/4→ convert back:(2×4+1)/4 = 9/4