How to Order Rational Numbers from Least to Greatest

📚 Quick Study Guide

🔢 Rational Numbers: Any number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. ➕ Positive Rational Numbers: Numbers greater than zero. They are located to the right of zero on the number line. ➖ Negative Rational Numbers: Numbers less than zero. They are located to the left of zero on the number line. 🧭 Zero: Zero is a rational number ($\frac{0}{1}$) and is neither positive nor negative. It separates positive and negative numbers on the number line. ⚖️ Comparing Rational Numbers:
📈 Common Denominator: Convert fractions to have the same denominator, then compare numerators. ➗ Decimal Conversion: Convert fractions to decimals for easier comparison. 📏 Number Line: Visualize the numbers on a number line; numbers to the left are smaller.

Practice Quiz

1. Which of the following rational numbers is the smallest?
   1. $\frac{1}{2}$
   2. $-\frac{1}{4}$
   3. $\frac{1}{8}$
   4. $-\frac{1}{2}$
2. Order the following rational numbers from least to greatest: $-\frac{2}{3}$, $\frac{1}{2}$, $-\frac{1}{4}$, $0$.
   1. $\frac{1}{2}$, $-\frac{1}{4}$, $0$, $-\frac{2}{3}$
   2. $-\frac{2}{3}$, $-\frac{1}{4}$, $0$, $\frac{1}{2}$
   3. $0$, $\frac{1}{2}$, $-\frac{1}{4}$, $-\frac{2}{3}$
   4. $-\frac{1}{4}$, $-\frac{2}{3}$, $0$, $\frac{1}{2}$
3. Which rational number is greater: $-\frac{3}{5}$ or $-\frac{4}{5}$?
   1. $-\frac{3}{5}$
   2. $-\frac{4}{5}$
   3. They are equal
   4. Cannot be determined
4. Which of the following is the largest rational number?
   1. $0.25$
   2. $-0.5$
   3. $0.1$
   4. $-0.75$
5. Order the following decimals from least to greatest: $0.6$, $-0.8$, $0.2$, $-0.1$.
   1. $-0.8$, $-0.1$, $0.2$, $0.6$
   2. $0.6$, $0.2$, $-0.1$, $-0.8$
   3. $-0.1$, $-0.8$, $0.2$, $0.6$
   4. $0.2$, $0.6$, $-0.8$, $-0.1$
6. Which of the following fractions is equivalent to a number between 0 and 1?
   1. $\frac{5}{4}$
   2. $\frac{7}{6}$
   3. $\frac{2}{3}$
   4. $\frac{9}{8}$
7. Arrange these numbers from least to greatest: $-\frac{5}{2}$, $1.5$, $-\frac{1}{2}$, $2$.
   1. $2$, $1.5$, $-\frac{1}{2}$, $-\frac{5}{2}$
   2. $-\frac{5}{2}$, $-\frac{1}{2}$, $1.5$, $2$
   3. $1.5$, $2$, $-\frac{5}{2}$, $-\frac{1}{2}$
   4. $-\frac{1}{2}$, $-\frac{5}{2}$, $1.5$, $2$