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Multiply multiple numbers with step-by-step solutions. Supports decimals, negative numbers, partial products for long multiplication, and scientific notation for large results.
Enter at least 2 numbers to calculate
Examples:
12 × 5 = 60
2.5 × 4 × 3 = 30
Multiplication is one of the four basic arithmetic operations, along with addition, subtraction, and division. It represents repeated addition of the same number. When you multiply two numbers, you're finding the total of one number added to itself a certain number of times.
For example, 4 × 3 means "add 4 to itself 3 times": 4 + 4 + 4 = 12. The first number is called the multiplicand, the second is the multiplier, and the result is the product.
Multiplication can be represented by several symbols: × (times sign), · (dot), or * (asterisk). In algebra, numbers placed next to each other (like 3x) also indicate multiplication.
5 × 8 = 40
Five groups of eight equals forty
3 boxes × 12 items = 36 total items
Three boxes with twelve items each
a × b = b × a
The order of multiplication doesn't matter. You get the same result regardless of which number comes first.
Example: 3 × 5 = 5 × 3 = 15
(a × b) × c = a × (b × c)
When multiplying three or more numbers, the grouping doesn't affect the result.
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24
a × (b + c) = (a × b) + (a × c)
Multiplication distributes over addition. You can multiply each term separately and then add.
Example: 3 × (4 + 5) = (3 × 4) + (3 × 5) = 27
a × 1 = a
Any number multiplied by 1 remains unchanged. One is the multiplicative identity.
Example: 42 × 1 = 42
a × 0 = 0
Any number multiplied by zero equals zero. Zero groups of anything is nothing.
Example: 1000 × 0 = 0
(-a) × (-b) = a × b
(-a) × b = -(a × b)
Negative times negative equals positive. Negative times positive equals negative.
Example: -3 × -4 = 12, -3 × 4 = -12
Simply add zeros to the end of the number. For decimals, move the decimal point to the right.
Multiply by 10, then divide by 2. Or divide by 2, then multiply by 10.
16 × 5 = (16 × 10) ÷ 2 = 160 ÷ 2 = 80
Multiply by 10, then subtract the original number.
7 × 9 = (7 × 10) - 7 = 70 - 7 = 63
Add the two digits and place the sum in the middle. If sum is 10+, carry the 1.
43 × 11: 4 + 3 = 7, so 4-7-3 = 473
67 × 11: 6 + 7 = 13, so 6+1-3-7 = 737
Multiply the first digit by (itself + 1), then append 25.
25² = 2 × 3 = 6, then 625
65² = 6 × 7 = 42, then 4225
Use the distributive property to break complex multiplications into simpler ones.
14 × 6 = (10 + 4) × 6 = 60 + 24 = 84
23 × 7 = (20 + 3) × 7 = 140 + 21 = 161
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 original numbers and place the decimal point in your answer so it has that many decimal places. For example, 2.5 × 3.2: multiply 25 × 32 = 800, then since there are 2 decimal places total (one in each number), place the decimal to get 8.00 = 8.
When multiplying negative numbers, follow these rules: negative × negative = positive, negative × positive = negative, and positive × positive = positive. For example: (-3) × (-4) = 12, (-3) × 4 = -12, and 3 × 4 = 12. The rule "two negatives make a positive" only applies when multiplying or dividing, not when adding or subtracting.
For large numbers, use long multiplication: multiply the first number by each digit of the second number, starting from the rightmost digit. Each result is a partial product, shifted one place to the left. Finally, add all partial products together. Alternatively, break large numbers into smaller parts using the distributive property: 23 × 45 = 23 × (40 + 5) = (23 × 40) + (23 × 5) = 920 + 115 = 1035.
Addition combines quantities of the same units, while multiplication represents repeated addition. Addition is simpler but slower for large quantities. For example, adding 5 ten times (5+5+5+5+5+5+5+5+5+5) equals 50, but multiplication gives the same result more efficiently: 5 × 10 = 50. Multiplication is essential for calculating areas, volumes, and scaling quantities.
To multiply multiple numbers, multiply them in any order (thanks to the commutative and associative properties). You can work left to right, multiply the first two numbers, then multiply that result by the third number, and so on. For example, 2 × 3 × 4 × 5: start with 2 × 3 = 6, then 6 × 4 = 24, then 24 × 5 = 120. You can also group numbers strategically to make mental math easier.
Scientific notation expresses very large or very small numbers in the form a × 10^n, where 1 ≤ a < 10 and n is an integer. For example, 3,000,000 = 3 × 10^6, and 0.00042 = 4.2 × 10^(-4). It's commonly used in science, engineering, and mathematics when dealing with astronomical distances, microscopic measurements, or when precision is important with very large or small values. Our calculator automatically displays results in scientific notation when they exceed 1 million or are smaller than 0.001.
Multiplication is a fundamental mathematical operation that extends the concept of repeated addition. Throughout history, multiplication has been essential for commerce, construction, astronomy, and countless other fields. Ancient civilizations developed various methods for multiplication, from Egyptian doubling methods to the lattice method used in medieval times.
Multiplying simple numbers: 5 × 8 = 40. This is the most basic form we learn first.
Used in linear algebra, combines rows and columns of matrices for transformations and data analysis.
Includes dot product and cross product, essential in physics and engineering for force and direction calculations.
Multiplying numbers with real and imaginary parts, crucial in electrical engineering and quantum physics.
Different cultures developed unique multiplication methods. The ancient Egyptians used a doubling method, repeatedly doubling numbers and adding appropriate values. Russian peasants used a similar technique. The lattice method, also called gelosia multiplication, was popular in medieval Europe and is still taught today as an alternative to standard long multiplication. Each method has its advantages and offers insight into how humans have approached mathematical problems throughout history.