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Think of adding or subtracting fractions as a bit like adding or subtracting apples and oranges. You can't add 1 apple to 2 oranges unless you call each of them "pieces of fruit." Then if you added them, you'd have 3 pieces of fruit. Similarly you can't add 1/4 to 1/3 unless you re-name each fraction such that they have the same denominator: 1/4 becomes 3/12, and 1/3 becomes 4/12. Adding them together simply involves adding the numerators to get 7/12. Subtracting is similar, except you subtract one numerator from the other.
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