Fraction
Oh, fractions — back when our biggest problem was splitting a pizza fairly..
Reciprocal: A Special Fraction
Tips: The larger the number, the smaller the reciprocal -- just watch out for negative numbers!
1986 AJHSME: Problem 2
1988 AJHSME: Problem 15
1989 AJHSME: Problem 18
Simple Fraction Problems
1985 AJHSME: Problem 5 Problem 10
1986 AJHSME: Problem 6 Problem 14
1987 AJHSME: Problem 11 Problem 12 Problem 21
1988 AJHSME: Problem 3
1989 AJHSME: Problem 2 Problem 12 Problem 13
1990 AJHSME: Problem 6
1991 AJHSME: Problem 2
1992 AJHSME: Problem 2 Problem 14 Problem 25
1993 AJHSME: Problem 2 Problem 16
1994 AJHSME: Problem 2 Problem 13
2006 AMC 8: Problem 4
2008 AMC 8: Problem 7
2010 AMC 8: Problem 10
2012 AMC 8: Problem 4
2024 AMC 8: Problem 2
Not So Simple Fraction Problems
1994 AJHSME: Problem 20
2002 AMC 8: Problem 25
2004 AMC 8: Problem 16 Problem 20
2010 AMC 8: Problem 20
2011 AMC 8: Problem 14
2015 AMC 8: Problem 16
2016 AMC 8: Problem 12
2019 AMC 8: Problem 15 Problem 23
2023 AMC 8: Problem 10
2024 AMC 8: Problem 19
2025 AMC 8: Problem 17 Problem 20
Hard Fraction Problems
2022 AIME I: Problem 7
2023 AIME II: Problem 5
Comparing Fractions
Tips: just bear in mind a few simple rules:Same numerator, fraction with a larger denominator is smaller
Same denominator, fraction with a smaller numerator is smaller
Same difference between denominator and numerator, fraction with larger numbers is bigger (assuming they are less than 1. Otherwise, the conclusion is reversed)
If two fractions share nothing in common, cross-multiplying them, whichever side ends up bigger is bigger
1987 AJHSME: Problem 13
1994 AJHSME: Problem 1
2012 AMC 8: Problem 20
2019 AMC 8: Problem 3
Fraction Word Problems
1987 AJHSME: Problem 18
2025 AMC 8: Problem 17