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This lesson extends the work on fractions and recurring decimals to cover complex fraction operations and the algebraic proof that recurring decimals are rational. These are Higher-tier topics in the Edexcel GCSE Mathematics (1MA1) specification and are commonly tested on all three papers.
| Term | Meaning |
|---|---|
| Proper fraction | A fraction where the numerator is less than the denominator, e.g. 3/5 |
| Improper fraction | A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4 |
| Mixed number | A whole number and a fraction combined, e.g. 1 3/4 |
| Reciprocal | The reciprocal of a/b is b/a; the reciprocal of n is 1/n |
| Rational number | Any number that can be expressed as p/q where p, q are integers and q ≠ 0 |
To add or subtract fractions, they must have a common denominator.
Calculate 3/4 + 2/5
LCD of 4 and 5 is 20.
3/4 = 15/20
2/5 = 8/20
15/20 + 8/20 = 23/20 = 1 3/20
Answer: 23/20 or 1 3/20
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