Number & Operations in Base Ten

Multiplying Multi-Digit Numbers

Multiplying a multi-digit number by a one-digit number.

Intermediate20 min lesson2 min readUpdated August 12, 2026Author not yet attributed

Multiplying Bigger Numbers

Multiplying a multi-digit number by a one-digit number uses the same distributive property from Grade 3, applied to place value. Breaking the larger number apart by place value turns one hard multiplication into a few easy ones, added together.

To multiply a number like 342 by 6, break 342 into its place-value parts — 300, 40, and 2 — multiply each part by 6 separately, and add the three results together. This is called finding partial products.

Worked Example — Multiplying Using Partial Products

Multiply 342 × 6. Break 342 into 300, 40, and 2. Multiply each part: 300 × 6 = 1,800, 40 × 6 = 240, 2 × 6 = 12. Add the partial products: 1,800 + 240 + 12 = 2,052. So 342 × 6 = 2,052.

Worked Example — Checking with Estimation

Estimate 342 × 6 by rounding 342 to 300 first: 300 × 6 = 1,800. The exact answer, 2,052, is reasonably close to this estimate, confirming the exact calculation is likely correct.

342 \times 6 = (300 \times 6) + (40 \times 6) + (2 \times 6) = 1{,}800 + 240 + 12 = 2{,}052

Tip

Always estimate first by rounding the multi-digit number to its leading place value — it gives a fast reasonableness check for the exact answer found afterward.

Common Mistakes

Forgetting to include a place value's zeros when breaking a number apart, such as treating the '4' in 342's tens place as just 4 instead of 40.
Break the number apart by its true place value — the tens digit of 342 represents 40, not 4, and must be multiplied as 40 for the partial product to be correct.
Adding the partial products incorrectly, especially misaligning them by place value.
Line up the partial products by place value before adding, the same way any multi-digit addition problem is lined up.

Key Takeaways

Multiplying a multi-digit number by a one-digit number can be done by breaking the larger number into place-value parts.
Each part is multiplied separately, producing partial products, which are then added together.
Estimating first, by rounding, checks whether the exact answer is reasonable.

Summary

Partial products break a hard multiplication into several easy ones. The next lesson applies a related strategy — partial quotients — to divide multi-digit numbers.

Track your progress

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