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Long Multiply Calculator – Step-by-Step Work (2025)

Long Multiply Calculator – Step-by-Step Work (2025)

Looking for a Long Multiply Calculator? This guide shows the **standard long multiplication** method with clear working lines so you can learn the process and check your answers. Updated for 2025. Works for multi-digit numbers, decimals, and negatives.

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What Is Long Multiplication?

Long multiplication breaks a big product into partial products by place value (ones, tens, hundreds, …) and then adds them up. It’s reliable, transparent, and easy to check with estimation.

Takeaway: Multiply each digit, write the partial products in rows, shift left for tens/hundreds, then add.

Step-by-Step Rules (Standard Algorithm)

  1. Write factors in columns with the longer number on top.
  2. Multiply rightmost digit of the bottom number by each digit of the top number, moving left. Carry as needed.
  3. Write the partial product on its own line.
  4. Shift one place left (add a trailing zero) for each step as you move to the next digit of the bottom number.
  5. Add all partial products to get the final result.
  6. Decimals: Count total decimal places in both factors; place that many in the final product.
  7. Signs: Same signs → positive; different signs → negative.
Pro Tip: Estimate first (e.g., 298×41 ≈ 300×40=12,000) to sanity-check the final sum.

Worked Example #1 — 347 × 26

  1. 6×347 = 2,082 (write 2,082)
  2. 2×347 (for “20”) = 694 → shift one place → 6,940
  3. Add: 2,082 + 6,940 = 9,022

Answer: 347 × 26 = 9,022

Check: Estimate 350×30=10,500 (close and reasonable).

Worked Example #2 — 12.8 × 3.4 (Decimals)

  1. Ignore decimals: 128 × 34 = 4,352
  2. Count decimal places: 12.8 (1) + 3.4 (1) = 2 places total
  3. Place decimal in product: 43.52

Answer: 12.8 × 3.4 = 43.52

Quick Tip: Always set the decimal at the end—don’t try to track it mid-multiplication.

Worked Example #3 — (−245) × 18 (Negatives)

  1. Multiply absolute values: 245 × 18 = 4,410
  2. Apply sign: one negative factor → product is negative

Answer: −4,410

Common Mistakes (and Easy Fixes)

  • Forgetting the shift zero when moving to the tens/hundreds digit → partial products won’t align.
  • Dropping carries in multi-digit rows → write carries clearly above the next column.
  • Decimal misplacement → count total decimal places at the end, then place them in the product.
  • No estimation → quick rounding avoids off-by-ten errors.
Takeaway: Line up digits, track carries, shift properly, and place decimals at the end.

Alternative: Box (Area) Method

Break numbers by place value (e.g., 347 = 300 + 40 + 7; 26 = 20 + 6), draw a grid, multiply each cell, then add the cell totals. It’s the same math, just more visual—great for teaching.

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FAQ: Long Multiply Calculator

How do I handle decimals in long multiplication?

Multiply as if they’re whole numbers, then place the decimal by counting the total decimal places in both factors.

Do I need to write a zero when I move to the tens place?

Yes. Each new row shifts one place left (append a zero) before adding the partial products.

What’s the fastest way to check?

Estimate with rounded numbers and compare. You can also reverse with division if needed.

Does the sign matter?

Yes: same signs → positive product; different signs → negative product.

Is the box/area method the same as long multiplication?

Yes—the area method restructures the same place-value products in a grid. The final sum is identical.

© LongDivisionMath.com • Updated 2025