Test your knowledge: ordering mixed numbers and improper fractions

📚 Quick Study Guide

• 🔢 Mixed Number: A number consisting of a whole number and a proper fraction (e.g., $2\frac{1}{3}$).
• ➗ Improper Fraction: A fraction where the numerator (top number) is greater than or equal to the denominator (bottom number) (e.g., $\frac{7}{3}$).
• 🔄 Converting Mixed Number to Improper Fraction: Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, $2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$.
• ➗ Converting Improper Fraction to Mixed Number: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. For example, $\frac{7}{3} = 2\frac{1}{3}$ (7 divided by 3 is 2 with a remainder of 1).
• ⚖️ Comparing Fractions: To compare, the fractions must have a common denominator. Find the least common multiple (LCM) of the denominators and convert each fraction.

Practice Quiz

1. What is the improper fraction equivalent of $3\frac{2}{5}$?
   1. $\frac{10}{5}$
   2. $\frac{17}{5}$
   3. $\frac{13}{5}$
   4. $\frac{8}{5}$
2. Which of the following is greater: $2\frac{1}{4}$ or $\frac{10}{4}$?
   1. $2\frac{1}{4}$
   2. $\frac{10}{4}$
   3. They are equal
   4. Cannot be determined
3. Convert $\frac{15}{4}$ to a mixed number.
   1. $4\frac{1}{4}$
   2. $3\frac{3}{4}$
   3. $2\frac{7}{4}$
   4. $1\frac{11}{4}$
4. Which fraction is the smallest: $\frac{5}{2}$, $2\frac{1}{3}$, or $\frac{7}{3}$?
   1. $\frac{5}{2}$
   2. $2\frac{1}{3}$
   3. $\frac{7}{3}$
   4. They are all equal
5. Which of the following is equivalent to $\frac{20}{6}$?
   1. $2\frac{2}{6}$
   2. $3\frac{1}{3}$
   3. $3\frac{2}{6}$
   4. $4\frac{2}{6}$
6. Order the following from least to greatest: $\frac{8}{3}$, $2\frac{1}{6}$, $\frac{5}{2}$.
   1. $\frac{8}{3}$, $\frac{5}{2}$, $2\frac{1}{6}$
   2. $2\frac{1}{6}$, $\frac{8}{3}$, $\frac{5}{2}$
   3. $\frac{5}{2}$, $\frac{8}{3}$, $2\frac{1}{6}$
   4. $2\frac{1}{6}$, $\frac{5}{2}$, $\frac{8}{3}$
7. What is $1\frac{1}{2}$ as an improper fraction?
   1. $\frac{2}{2}$
   2. $\frac{3}{2}$
   3. $\frac{4}{2}$
   4. $\frac{1}{2}$