Steps to order mixed numbers and improper fractions from least to greatest

📚 Quick Study Guide

• 🔍 Convert mixed numbers to improper fractions: Multiply the whole number by the denominator, add the numerator, and keep the same denominator.
• ➗ Understand improper fractions: These have a numerator larger than or equal to the denominator.
• ✍️ Find a common denominator: To compare fractions, they need the same denominator. Find the least common multiple (LCM) of the denominators.
• ➕ Convert fractions to equivalent fractions with the common denominator: Multiply both the numerator and denominator by the same number to get the common denominator.
• 🔢 Compare the numerators: Once the denominators are the same, the fraction with the smallest numerator is the smallest fraction.
• 📌 Order the fractions: Arrange the fractions from the smallest to largest numerator.
• 🔄 Convert back (if needed): If the original question included mixed numbers, convert the improper fraction answers back to mixed numbers at the end.

Practice Quiz

1. Question 1: Which of the following is the smallest fraction? $2\frac{1}{2}$, $\frac{7}{3}$, $\frac{5}{2}$, $2\frac{1}{4}$
   1. $2\frac{1}{2}$
   2. $\frac{7}{3}$
   3. $\frac{5}{2}$
   4. $2\frac{1}{4}$
2. Question 2: Order from least to greatest: $\frac{9}{4}$, $2\frac{1}{3}$, $\frac{5}{2}$
   1. $\frac{5}{2}$, $\frac{9}{4}$, $2\frac{1}{3}$
   2. $\frac{9}{4}$, $\frac{5}{2}$, $2\frac{1}{3}$
   3. $2\frac{1}{3}$, $\frac{9}{4}$, $\frac{5}{2}$
   4. $2\frac{1}{3}$, $\frac{5}{2}$, $\frac{9}{4}$
3. Question 3: Which fraction is the largest? $\frac{11}{5}$, $2\frac{1}{5}$, $\frac{9}{4}$
   1. $\frac{11}{5}$
   2. $2\frac{1}{5}$
   3. $\frac{9}{4}$
   4. They are all equal
4. Question 4: Order $\frac{7}{6}$, $1\frac{1}{3}$, and $\frac{4}{3}$ from least to greatest.
   1. $\frac{7}{6}$, $1\frac{1}{3}$, $\frac{4}{3}$
   2. $1\frac{1}{3}$, $\frac{7}{6}$, $\frac{4}{3}$
   3. $\frac{4}{3}$, $\frac{7}{6}$, $1\frac{1}{3}$
   4. $\frac{7}{6}$, $\frac{4}{3}$, $1\frac{1}{3}$
5. Question 5: Which of the following is the correct order from least to greatest: $\frac{8}{5}$, $1\frac{2}{5}$, $\frac{3}{2}$?
   1. $\frac{8}{5}$, $1\frac{2}{5}$, $\frac{3}{2}$
   2. $\frac{3}{2}$, $\frac{8}{5}$, $1\frac{2}{5}$
   3. $1\frac{2}{5}$, $\frac{8}{5}$, $\frac{3}{2}$
   4. $1\frac{2}{5}$, $\frac{3}{2}$, $\frac{8}{5}$
6. Question 6: Order the following from least to greatest: $\frac{5}{3}$, $1\frac{1}{6}$, $\frac{7}{4}$
   1. $\frac{5}{3}$, $\frac{7}{4}$, $1\frac{1}{6}$
   2. $1\frac{1}{6}$, $\frac{5}{3}$, $\frac{7}{4}$
   3. $\frac{7}{4}$, $\frac{5}{3}$, $1\frac{1}{6}$
   4. $1\frac{1}{6}$, $\frac{7}{4}$, $\frac{5}{3}$
7. Question 7: Which list is in order from least to greatest? $\frac{10}{7}$, $1\frac{1}{8}$, $\frac{6}{5}$
   1. $\frac{10}{7}$, $1\frac{1}{8}$, $\frac{6}{5}$
   2. $1\frac{1}{8}$, $\frac{6}{5}$, $\frac{10}{7}$
   3. $\frac{6}{5}$, $\frac{10}{7}$, $1\frac{1}{8}$
   4. $\frac{6}{5}$, $1\frac{1}{8}$, $\frac{10}{7}$