To subtract fractions, make the denominators (bottom numbers) the same, subtract the numerators (top numbers), and keep the denominator. Matching denominators are easy: 5/8 − 2/8 = 3/8. Different denominators need a common denominator first: 3/4 − 2/5 = 15/20 − 8/20 = 7/20.
If the bottom numbers match, subtract the tops straight away. If not, you need a common denominator — fractions can only be subtracted when they're counted in the same-sized pieces.
Find the least common multiple of the two denominators, then scale each fraction up: multiply its top and bottom by the same number. For 3/4 − 2/5, the LCM of 4 and 5 is 20, so 3/4 = 15/20 and 2/5 = 8/20.
Subtract the top numbers and keep the denominator: 15/20 − 8/20 = 7/20. The denominator stays because you're still counting twentieths — just fewer of them.
Divide top and bottom by their greatest common factor. 7/20 is already in simplest form; something like 6/8 would simplify to 3/4.
Same denominators
5/8 − 2/8
Answer: 3/8
Different denominators
3/4 − 2/5
Answer: 7/20
Mixed numbers (with regrouping)
3 1/4 − 1 2/3
Answer: 1 7/12
3/4 − 2/5 is not 1/(−1) or 1/1. Denominators never get subtracted — they name the piece size. Match them first, then subtract only the tops.
In 1/4 − 2/3 the answer is negative (3/12 − 8/12 = −5/12). Students trained to "always take small from big" will flip the subtraction and get +5/12. Keep the order the question gives you.
In 3 1/4 − 1 2/3 you can't take 2/3 from 1/4 directly. Either convert both to improper fractions (safest), or regroup: borrow 1 from the 3 to make 2 5/4, then subtract parts.
Rewrite both fractions over a common denominator, then subtract the numerators. For 3/4 − 2/5, use twentieths: 15/20 − 8/20 = 7/20.
The most reliable route is converting both to improper fractions: 3 1/4 − 1 2/3 = 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12. You can also subtract wholes and fraction parts separately, borrowing a whole when the first fraction part is smaller.
When the fraction you're subtracting is bigger than the one you're subtracting from — like 1/4 minus 2/3 inside a mixed-number problem — you borrow 1 from the whole number and add it to the fraction as a full set of pieces: 3 1/4 becomes 2 + 1 + 1/4 = 2 5/4. Then the subtraction works piece by piece.
Yes, whenever the second fraction is larger: 1/4 − 2/3 = 3/12 − 8/12 = −5/12. That's a perfectly valid answer — just keep the sign.
Rewrite the whole number using the fraction's denominator. For 3 − 2/5, write 3 = 15/5, so 15/5 − 2/5 = 13/5 = 2 3/5. Equivalently: take one whole, split it into fifths, remove two of them.
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