Multiply two numbers with step-by-step long multiplication. See the complete working breakdown, handle decimals, and use the visual grid method for deeper understanding.
Click any example to load it into the calculator and see the long multiplication working.
12 × 34 = ?
Answer: 408
123 × 456 = ?
Answer: 56,088
25 × 4 = ?
Answer: 100
3.5 × 2.2 = ?
Answer: 7.70
100 × 1000 = ?
Answer: 100,000
999 × 999 = ?
Answer: 998,001
Multiplication is repeated addition. Multiplying a × b means adding a to itself b times. The result is called the product, the numbers being multiplied are factors or multiplicand (first) and multiplier (second).
Multiplication is commutative: a × b = b × a. It is also associative: (a × b) × c = a × (b × c).
The grid method (also called the box method) breaks multiplication into smaller, manageable parts by splitting each number into its place values and organizing them in a table.
Break each number into its place values. For example, 34 = 30 + 4 (tens + units). For larger numbers, include hundreds, thousands, etc.
Draw a table with the parts of the first number across the top and the parts of the second number down the side. Each cell will hold the product of its row and column headers.
Multiply each row header by each column header and write the result in the corresponding cell. For 12 × 34: 10×30=300, 10×4=40, 2×30=60, 2×4=8.
Sum all the values in the grid cells. The total is your product. For 12 × 34: 300 + 40 + 60 + 8 = 408.
| × | 40 | 7 | Total |
|---|---|---|---|
| 20 | 800 | 140 | 940 |
| 3 | 120 | 21 | 141 |
| Total | 920 | 161 | 1081 |
23 × 47 = 800 + 140 + 120 + 21 = 1,081
Mastering times tables up to 12×12 is the foundation of all multiplication. Practice with flashcards, songs, and daily drills. Once automatic, larger problems become much faster to solve.
To multiply by 10, add one zero. By 100, add two zeros. For decimals, move the decimal point right: one place per zero. Example: 3.5 × 100 = 350 (decimal moves 2 places right).
Use the distributive property: 7 × 48 = 7 × (40 + 8) = 7×40 + 7×8 = 280 + 56 = 336. This is especially useful for mental math with larger numbers.
Double one factor and halve the other: 25 × 16 = (25×2) × (16÷2) = 50 × 8 = 400. This works because the product stays the same and one of the factors becomes easier to work with.
Always estimate first: 48 × 52 ≈ 50 × 50 = 2,500. If your actual answer is far from 2,500, you know to recheck. The actual answer for 48 × 52 is 2,496 — very close!
×5: Half of ×10. 48×5 = 48×10÷2 = 240. ×9: ×10 minus the number. 48×9 = 480 − 48 = 432. ×11: For two-digit numbers, add digits and insert between them: 34×11 = 3_(3+4)_4 = 374.
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Multiplication is one of the four basic arithmetic operations. It represents repeated addition of the same number. For example, 4 × 3 means adding 4 three times: 4 + 4 + 4 = 12. The symbol for multiplication is × (times), but it can also be represented by a dot (·) or an asterisk (*).
In multiplication, the numbers being multiplied are called factors (or more specifically, the multiplicand and multiplier), and the result is called the product. Multiplication is a cornerstone of arithmetic and is essential for understanding more advanced mathematical concepts.
Long multiplication (also called the standard algorithm) is used for multiplying multi-digit numbers. Here's how it works:
To multiply decimals, first ignore the decimal points and multiply the numbers as if they were whole numbers. Then count the total number of decimal places in both factors combined. Place the decimal point in the product so that it has the same number of decimal places. For example, 3.5 (1 decimal place) × 2.2 (1 decimal place) = 7.70 (2 decimal places).
Multiplication is essential in countless real-world scenarios:
Our Multiplication Calculator is designed to help students, teachers, and professionals perform accurate multiplication with complete step-by-step working. Whether you're learning long multiplication for the first time, checking homework, or need a reliable tool for business calculations, this calculator provides clear, detailed results every time.
See the complete long multiplication process with every partial product shown. Perfect for students learning multiplication algorithms and anyone who wants to understand how multiplication works.
Works with whole numbers, decimals, large numbers, and small numbers. Automatic decimal placement and carry handling for every case.
Learn the visual grid/box method with clear explanations and examples. Build number sense by seeing how place values combine.
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Important Disclaimer: This Multiplication Calculator is designed for educational and general-purpose arithmetic use. While we strive for accuracy, please verify critical calculations independently. This tool is for informational and educational purposes only.