What is 333 times 135?

To multiply two numbers, split one factor into its place-value parts (hundreds, tens, and ones) and use the distributive property: multiply each part by the other factor separately, then add the partial products. Breaking a multiplication into these smaller pieces and summing every partial product together (each shifted to its correct place value) always gives the exact product.

1. Write 135 as its place-value parts: 100 + 30 + 5.

2. Multiply 333 by the hundreds part: 333 × 100 = 33300.

3. Multiply 333 by the tens part: 333 × 30 = 9990.

4. Multiply 333 by the ones part: 333 × 5 = 1665.

5. Add the three partial products: 33300 + 9990 + 1665 = 44955.

As an independent check, write 135 as 140 − 5 instead: 333 × 140 = 46620 and 333 × 5 = 1665, so 46620 − 1665 = 44955 — the same result, confirming the product.

So 333 × 135 = 44955.