Multiply two fractions
Multiplying fractions is simpler than you think! Unlike addition, you don't need common denominators. You just multiply straight across: top times top, and bottom times bottom. Easy!
Concept
Multiplying two fractions is one of the most straightforward fraction operations. **The Rule: Top x Top, Bottom x Bottom** To multiply two fractions, you simply: 1. **Multiply the numerators** (the top numbers) together. 2. **Multiply the denominators** (the bottom numbers) together. 3. **Simplify** the resulting fraction if possible. **Example: 2/3 x 4/5** 1. **Multiply the numerators:** 2 x 4 = 8 2. **Multiply the denominators:** 3 x 5 = 15 3. **Result:** 8/15 (This is already in simplest form). **Visualizing Multiplication: The Area Model** What does 2/3 x 4/5 actually mean? It means "What is 2/3 **of** 4/5?" 1. Draw a rectangle and divide it into 5 vertical columns. Shade 4 of them to show **4/5**. 2. Now, divide the same rectangle into 3 horizontal rows. Shade 2 of those rows to show **2/3**. 3. The part of the rectangle that is **double-shaded** is your answer. You will see 8 double-shaded squares out of a total of 15 squares. 4. This visually shows that 2/3 of 4/5 is **8/15**. **Simplifying Before You Multiply (Cross-Canceling)** This is a great shortcut! If a numerator and a denominator on opposite sides of the 'x' sign share a common factor, you can simplify them *before* you multiply. **Example: 3/4 x 2/9** 1. Look at the diagonals: 3 and 9 can both be divided by 3. * 3 ÷ 3 = 1 * 9 ÷ 3 = 3 2. Look at the other diagonals: 2 and 4 can both be divided by 2. * 2 ÷ 2 = 1 * 4 ÷ 2 = 2 3. Now rewrite your problem with the new simplified numbers: **1/2 x 1/3** 4. Multiply straight across: 1 x 1 = 1, and 2 x 3 = 6. 5. **Result: 1/6**. This is much easier than multiplying 3x2=6 and 4x9=36 to get 6/36 and then simplifying. **Key Idea:** When you multiply two proper fractions (fractions less than 1), the answer is always smaller than both of the original fractions. You are finding a part *of* a part.
Try it
Practice multiplying fractions! **Basic Multiplication:** 1. 1/2 x 3/5 = ? 2. 2/3 x 1/4 = ? 3. 3/4 x 5/6 = ? 4. 1/3 x 1/3 = ? **Simplify Your Answer:** 5. 2/5 x 5/6 = ? 6. 3/4 x 2/9 = ? (Try cross-canceling!) 7. 4/7 x 14/16 = ? **Word Problems:** 8. A recipe for one batch of cookies calls for 3/4 cup of flour. If you are only making 1/2 of a batch, how much flour do you need? 9. A park is 5/6 of a mile long. The playground takes up 2/3 of the park's length. What fraction of a mile long is the playground? 10. At a school, 7/8 of the students have pets. Of those students, 2/3 have a dog. What fraction of the students at the school have a dog? **Challenge Problems:** 11. 1/2 x 2/3 x 3/4 = ? (What do you notice about this pattern?) 12. A rectangle measures 3/4 of a meter by 5/6 of a meter. What is its area?