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It is usually easier to convert mixed numbers to improper fractions, do the subtraction (by finding equivalent fractions with the same denominator) and convert any resulting improper fraction to a mixed number:
4 1/4 - 7 1/2 = (4×4+1)/4 + (7×2+1)/2
= 17/4 - 15/2
= 17/4 - (15×2)/(2×2)
= 17/4 - 30/4
= (17-30)/4
= -13/4
= -(3×4+1)/4
= -3 1/4
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