Finding Partial Products- The 990 Example

What Are Partial Products?

Partial products is a multiplication strategy that breaks numbers apart by place value. Instead of doing one big multiplication, you split numbers into tens, hundreds, and so on, multiply each piece separately, then add the results together.

It works because multiplication distributes over addition. That's the math rule behind it. Once you see it in action, it's hard to unsee.

Why 990 Makes a Great Example

990 is almost 1000. That makes it easy to work with and easy to check your work. You can round it to 1000, multiply, then subtract the difference.

The number 990 also breaks down cleanly into 900 + 90. Both components are simple to multiply. No messy decimals, no awkward fractions.

How to Find Partial Products with 990

Here's the process:

• Step 1: Break 990 into 900 and 90
• Step 2: Multiply each part by your other number
• Step 3: Add the two products together

That's it. Three steps. The hard part is picking the right numbers to break apart, and 990 makes that obvious.

Example: 990 × 7

Break 990 into 900 + 90.

Multiply: 900 × 7 = 6,300

Multiply: 90 × 7 = 630

Add: 6,300 + 630 = 6,930

Quick check: 990 × 7 = (1000 × 7) - (10 × 7) = 7,000 - 70 = 6,930. Matches.

Example: 990 × 24

Break 990 into 900 + 90.

Multiply: 900 × 24 = 21,600

Multiply: 90 × 24 = 2,160

Add: 21,600 + 2,160 = 23,760

Check with rounding: 1000 × 24 = 24,000, minus 10 × 24 = 240, gives you 23,760. Correct.

Partial Products vs. Standard Algorithm

Here's how the two methods compare side by side for 990 × 24:

All three give the same answer. The partial products method just shows your work more explicitly. That's useful when teaching or when you need to debug your own thinking.

Common Mistakes

• Forgetting to add both products. You did the multiplication right, but you stopped after step two. Add them together.
• Breaking the number wrong. 990 is 900 + 90, not 99 + 0. Place value matters.
• Losing zeros. 900 × 7 is not 63. It's 6,300. Track your zeros through every step.

When This Method Helps

Partial products shine when you're multiplying numbers with zeros in them. It also helps when mental math feels overwhelming and you need to break things down.

If you're comfortable with the standard algorithm, you don't need to switch. But if you're stuck or teaching someone who is, partial products gives you a way to see what's actually happening under the hood.

Quick Reference: 990 × Numbers 1–12

Notice the pattern. Every answer ends in 0. That's because 990 always contributes at least one zero to the product.