Multiplication Calculator

Multiplication is a fast way to add the same number again and again. Instead of writing 4 + 4 + 4, you write 4 × 3 and get 12. The answer is called the product, and the numbers you multiply are called factors. This multiplication calculator multiplies any two numbers, including decimals and negative numbers, and shows the working so you can follow every step instead of only seeing the answer.

• Multiplicand: the number that is being multiplied (the first factor).
• Multiplier: the number that says how many times to take the multiplicand (the second factor).
• Product: the result of the multiplication.
• Factor: any number that is multiplied. In 6 × 7 = 42, both 6 and 7 are factors of 42.

For big numbers, schools teach long multiplication. You multiply the top number by each digit of the bottom number, starting from the right, and add up the rows. Take 347 × 26 as an example.

1. Write 347 on top and 26 underneath, with the units lined up.
2. Multiply 347 by the units digit 6: 347 × 6 = 2,082. Write 2,082 as the first row.
3. Multiply 347 by the tens digit 2. Because the 2 is really 20, shift one place to the left (add a zero): 347 × 2 = 694, so the row is 6,940.
4. Add the rows: 2,082 + 6,940 = 9,022.
5. So 347 × 26 = 9,022. Check it another way: 347 × 25 = 8,675, and one more 347 makes 9,022.

Type your own numbers into the calculator above and press Calculate. The step-by-step player under the result shows exactly this working, one row at a time, with Back, Next and Play buttons.

Ignore the decimal points and multiply as if the numbers were whole. Then count the decimal places in both factors and give the answer that many decimal places in total. For 1.5 × 0.2: 15 × 2 = 30. The factors have 1 + 1 = 2 decimal places, so the product is 0.30, which is 0.3.

• Positive × positive = positive. Example: 6 × 7 = 42.
• Negative × negative = positive. Example: (−6) × (−7) = 42.
• Positive × negative (or negative × positive) = negative. Example: (−6) × 7 = −42.
• Any number × 0 = 0. Example: (−6) × 0 = 0.

• Commutative property: the order does not matter. 7 × 8 = 8 × 7 = 56. That is why the times table is the same when you flip it.
• Associative property: grouping does not matter. (2 × 3) × 4 = 2 × (3 × 4) = 24.
• Distributive property: you can split a factor. 7 × 13 = 7 × (10 + 3) = 70 + 21 = 91. This is the idea behind the area model above.
• Identity property: any number × 1 stays the same. 245 × 1 = 245.
• Zero property: any number × 0 is 0.

• 12 × 8 = 96 (12 × 8 = 10 × 8 + 2 × 8 = 80 + 16).
• 25 × 16 = 400 (25 × 4 = 100, and 16 is four 4s, so 4 × 100).
• 0.4 × 0.5 = 0.2 (4 × 5 = 20, with two decimal places gives 0.20).
• (−9) × 6 = −54 (9 × 6 = 54, and the signs differ, so the answer is negative).
• 1,250 × 4 = 5,000 (double 1,250 twice: 2,500, then 5,000).

• Multiply by 10: move every digit one place left (add a zero). Multiply by 100: two places.
• Multiply by 5: multiply by 10 and halve the answer. 18 × 5 = 180 ÷ 2 = 90.
• Multiply by 9: multiply by 10 and subtract the number. 7 × 9 = 70 − 7 = 63.
• Multiply by 4: double, then double again. 15 × 4 = 30, then 60.
• Multiply by 11 (two digits): add the digits and put the sum in the middle. 23 × 11 = 2(2+3)3 = 253.

You multiply to find the area of a room (length × width), the total price of several items (price × quantity), a percentage of an amount (amount × 0.15 for 15%), the distance travelled (speed × time), and to scale a recipe for more people. Every one of these is the same operation: take one quantity as many times as another quantity says.