# How can you order rational numbers from least to greatest?

## Question:

How can you order rational numbers from least to greatest?

## Rational numbers:

Rational numbers are any number that can be expressed as a fraction. Because of this, all rational numbers possess a numerator value and a denominator value. All integers are rational numbers.

All rational numbers can be expressed as fractions, meaning that they all have numerators and denominators when in fractional form. To order rational numbers from least to greatest, all the numbers need to have a common denominator. To accomplish this, the least common multiple of all the denominators must be found. After all the fractions have a common denominator, the numerators can be compared to order the numbers from least to greatest. For example, a group of given rational numbers include 1/4, 8, 1/3, and 1/12. First, all the numbers must be expressed as fractions: 1/4, 8/1, 1/3, and 1/12. The least common multiple of the denominators 4, 1, 3, and 12 is 12. Therefore, all the rational numbers must be converted to numbers with a denominator of 12. In order for 1/4 to have a denominator of 12, both the numerator and denominator must be multiplied by 3. This produces a new fraction of 3/12. The numerator and denominator of 8/1 must be multiplied by 12 to have a denominator of 12. This causes the new fraction to be 96/12. For 1/3 to have a denominator of 12, the numerator and denominator must be multiplied by four, which produces the fraction 4/12. The fraction 1/12 already has a denominator of 12, so it can be left alone. Now, the numerators can be ordered from least to greatest as follows: 1<3<4<96. The numerators can be matched to the rational numbers and the rational numbers themselves can be ordered from least to greatest as follows: 1/12<3/12<4/12<96/12, which can be simplified to 1/12<1/4<1/3<8.

Comparing & Ordering Rational Numbers

from

Chapter 12 / Lesson 1
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Rational numbers, any number expressed in the division of two integers, can be compared and ordered to determine their size, even when the digits may appear larger or smaller. Follow the examples of comparing and ordering rational numbers to learn this concept.