Multiply two fractions

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.

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?