Arithmetic: Multiplying two fractions

Multiplying fractions is one of the easiest fraction operations because, unlike addition or subtraction, you don’t need a common denominator. Simply multiply the numerators (top numbers) and denominators (bottom numbers) and simplify if needed.

Steps to Multiply Two Fractions

Example: 2/3 x 4/5​

Step 1: Multiply the Numerators

Multiply the top numbers:

$$2 \times 4 = 8$$

Step 2: Multiply the Denominators

Multiply the bottom numbers:

$$3 \times 5 = 15$$

Step 3: Write the Answer

8/15​

Since 8 and 15 have no common factors, this fraction is already in its simplest form.

✅ Final Answer: 8/15​

Multiplying Mixed Numbers

If you have mixed numbers, first convert them to improper fractions before multiplying.

Example: 

​2 1/3 x 1 2/5

Step 1: Convert to Improper Fractions

• 7/3​
• 7/5

Step 2: Multiply

7/3 x 7/5 = 49/15​

Step 3: Convert Back to a Mixed Number

49/15 = 3 4/15​​

Shortcut: Cross-Simplification

If possible, simplify before multiplying to make calculations easier.

Example: 6/8 x 4/9​

Instead of multiplying directly:​

• Simplify 6/8 to 3/4​
• No need to simplify 4/9​

Now multiply:

3/4×4/9​=12/36​

Now simplify 12/36 to 1/3.

✅ Final Answer: 1/3​

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