Fractions contain a top number called the numerator and a bottom number called the denominator separated by a horizontal line that represents division. In a proper fraction, the numerator is smaller than the denominator and thus represents a part of a whole (the denominator). While it is easy to tell which integers are larger or smaller than each other based on their position on the number line, it can be harder to determine where fractions fall and whether one fraction is less than or greater than another fraction.

Compare fractions with the same denominator by determining the relationship between the numerators. For example, 3/5 is less than 4/5 because 3 is less than 4.

Compare fractions with different denominators by finding the least common denominators and converting the fractions to it so the numerators can be compared. Determine whether 8/15 is less than or equal to 4/5. Note that because 5 is a multiple of 15, the least common denominator is 15. Convert the fractions: 8/15 remains the same and 4/5 becomes 12/15. Write that 8/15 is less than 4/5 since the 8 is smaller than the 12.

Use a calculator to find the decimal forms of very large fractions or those that don't have a common denominator to compare the sizes. Determine whether 3/17 is less than or greater than 5/13. Perform the divisions: 3/17 = 0.177 (rounded) and 5/13 = 0.385 (rounded). Write that 3/17 is smaller than 5/13 because that decimal form is smaller than the other.

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