Test Questions for Comparing and Ordering Fractions (6th Grade)

📚 Quick Study Guide

• 🍕Understanding Fractions: A fraction represents a part of a whole. It has a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.
• 🍎Comparing Fractions with the Same Denominator: When fractions have the same denominator, the fraction with the larger numerator is the larger fraction. For example, $\frac{3}{5} > \frac{1}{5}$ because 3 is greater than 1.
• 🍊Comparing Fractions with the Same Numerator: When fractions have the same numerator, the fraction with the smaller denominator is the larger fraction. For example, $\frac{2}{3} > \frac{2}{5}$ because 3 is smaller than 5.
• 🍋Comparing Fractions with Different Numerators and Denominators: To compare fractions with different numerators and denominators, you need to find a common denominator. This means finding a number that both denominators divide into evenly. Then, convert both fractions to have this common denominator. Finally, compare the numerators.
• 🍉Finding a Common Denominator: The easiest way to find a common denominator is to multiply the two denominators together. However, sometimes you can find a smaller common denominator (the least common multiple or LCM).
• 🍇Converting Fractions to Equivalent Fractions: To convert a fraction to an equivalent fraction with a different denominator, multiply both the numerator and denominator by the same number. For example, to convert $\frac{1}{2}$ to a fraction with a denominator of 6, multiply both the numerator and denominator by 3: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
• 💡Ordering Fractions: Once you can compare fractions, you can order a set of fractions from least to greatest or greatest to least. First, convert all fractions to have a common denominator. Then, order the fractions based on their numerators.

📝 Practice Quiz

1. Which fraction is the largest?
   1. $\frac{1}{4}$
   2. $\frac{1}{2}$
   3. $\frac{1}{3}$
   4. $\frac{1}{5}$
2. Which fraction is the smallest?
   1. $\frac{2}{5}$
   2. $\frac{2}{3}$
   3. $\frac{2}{7}$
   4. $\frac{2}{4}$
3. Which of the following fractions is greater than $\frac{1}{2}$?
   1. $\frac{3}{8}$
   2. $\frac{4}{10}$
   3. $\frac{5}{9}$
   4. $\frac{2}{5}$
4. Which of the following fractions is less than $\frac{1}{3}$?
   1. $\frac{2}{6}$
   2. $\frac{3}{8}$
   3. $\frac{1}{4}$
   4. $\frac{4}{11}$
5. Which list of fractions is ordered from least to greatest?
   1. $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$
   2. $\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$
   3. $\frac{1}{2}, \frac{1}{4}, \frac{1}{3}$
   4. $\frac{1}{3}, \frac{1}{2}, \frac{1}{4}$
6. Which of the following fractions is equivalent to $\frac{2}{3}$?
   1. $\frac{3}{4}$
   2. $\frac{4}{9}$
   3. $\frac{6}{9}$
   4. $\frac{8}{10}$
7. Which fraction is the largest: $\frac{3}{4}$, $\frac{5}{8}$, $\frac{1}{2}$, or $\frac{7}{16}$?
   1. $\frac{3}{4}$
   2. $\frac{5}{8}$
   3. $\frac{1}{2}$
   4. $\frac{7}{16}$