Test questions for multiplying proper fractions (area model & algorithm).

📚 Quick Study Guide

🔢 Proper Fractions: A fraction where the numerator (top number) is less than the denominator (bottom number), e.g., $\frac{2}{3}$. 📐 Area Model: A visual representation of multiplication where the fractions are represented as areas within a rectangle. The area of the overlapping region shows the product. ✖️ Multiplying Fractions Algorithm: To multiply fractions, multiply the numerators together and the denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. ✏️ Simplifying Fractions: Always simplify your answer to its lowest terms. Find the greatest common factor (GCF) of the numerator and denominator and divide both by it. 💡 Tips: When using the area model, ensure your rectangle's sides are divided according to the denominators of the fractions you're multiplying.

Practice Quiz

1. What is $\frac{1}{2} \times \frac{1}{3}$ using the algorithm?
   1. $\frac{2}{5}$
   2. $\frac{1}{6}$
   3. $\frac{2}{6}$
   4. $\frac{1}{5}$
2. Using the area model, if one side of the rectangle is divided into 4 equal parts and shaded to represent $\frac{3}{4}$, and the other side is divided into 3 equal parts and shaded to represent $\frac{2}{3}$, what fraction of the whole rectangle is double-shaded?
   1. $\frac{5}{7}$
   2. $\frac{6}{12}$
   3. $\frac{5}{12}$
   4. $\frac{1}{2}$
3. Calculate $\frac{2}{5} \times \frac{3}{4}$ and simplify your answer.
   1. $\frac{6}{20}$, Simplified: $\frac{3}{10}$
   2. $\frac{5}{9}$
   3. $\frac{6}{9}$, Simplified: $\frac{2}{3}$
   4. $\frac{5}{20}$, Simplified: $\frac{1}{4}$
4. What is $\frac{1}{4} \times \frac{2}{5}$?
   1. $\frac{3}{9}$, Simplified: $\frac{1}{3}$
   2. $\frac{2}{9}$
   3. $\frac{2}{20}$, Simplified: $\frac{1}{10}$
   4. $\frac{3}{20}$
5. Representing $\frac{2}{3} \times \frac{1}{2}$ with an area model, what fraction does the overlapping area represent?
   1. $\frac{3}{5}$
   2. $\frac{2}{6}$, Simplified: $\frac{1}{3}$
   3. $\frac{3}{6}$, Simplified: $\frac{1}{2}$
   4. $\frac{1}{5}$
6. If you need to find half of $\frac{3}{5}$, which multiplication problem would you use?
   1. $\frac{1}{2} + \frac{3}{5}$
   2. $\frac{1}{2} \times \frac{3}{5}$
   3. $\frac{2}{1} \times \frac{3}{5}$
   4. $\frac{3}{5} \div \frac{1}{2}$
7. What is the product of $\frac{4}{7} \times \frac{1}{3}$?
   1. $\frac{5}{10}$, Simplified: $\frac{1}{2}$
   2. $\frac{4}{21}$
   3. $\frac{5}{21}$
   4. $\frac{3}{10}$