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Comparing and Ordering Rational Numbers

Comparing rational numbers means deciding which of two is greater; ordering a list means arranging them from least to greatest. Learn to convert fractions and decimals to a common form to compare them, use a number line to order a full list, and handle negative rational numbers correctly.

What it means to compare rational numbers

A rational number is any number that can be written as a fraction of two integers, including whole numbers, fractions, and terminating or repeating decimals. To compare two rational numbers means to decide which is greater, and to order a list means to arrange them from least to greatest (or the reverse).

Rational numbers in order from least to greatest: −1½, −¾, 0, ½, 1¼.

Comparing using a common form

The most reliable way to compare rational numbers is to put them in the same form — usually decimals, since they line up naturally. Converting −¾ to −0.75 makes it easy to see it sits between −1.5 and 0. The rule that matters most is direction: on a number line, numbers get larger moving right and smaller moving left, so any negative number is always less than any positive number.

Ordering a list

To order several rational numbers, convert them all to the same form, then read their positions from left (least) to right (greatest) on a number line, as in the example above: −1½ < −¾ < 0 < ½ < 1¼.

Comparing negative rational numbers

Negative numbers can be the trickiest part: −1½ is less than −¾, even though 1½ looks like the "bigger" number, because −1½ sits farther to the left. The number closer to zero on the negative side is always the greater value — the same reasoning used when finding the square root of a rational number.

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Basic Math