14 Fun Facts About Multiplication

Which property of multiplication states that changing the order of the factors does not change the product?

The Commutative Property of Multiplication states that the product remains the same regardless of the order in which the factors are multiplied. For example, 3 × 4 yields the same result as 4 × 3.

What is the result obtained when two or more numbers are multiplied together?

In mathematics, the term 'product' refers to the result you get after multiplying numbers together. The numbers being multiplied are known as factors.

What are the numbers that are multiplied together to get a product called?

In a multiplication operation, the individual numbers that are being multiplied to reach a product are called factors.

Which property allows for the regrouping of numbers in a multiplication problem without changing the final product?

The Associative Property of Multiplication states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the final product.

What is the name of the property that relates multiplication to addition or subtraction, allowing a factor to be distributed to each term inside parentheses?

The Distributive Property allows a number outside parentheses to be multiplied by each term inside, simplifying expressions like a(b + c) to ab + ac.

Which mathematician is widely credited with introducing the '×' symbol for multiplication in 1631?

The '×' symbol for multiplication was introduced by British mathematician William Oughtred in his 1631 algebra text, 'Clavis Mathematicae'.

What alternative multiplication method involves drawing a grid and placing digits along the top and right side, then summing numbers along diagonals?

Lattice multiplication, also known by names like the Italian or Chinese method, is a systematic approach that uses a grid with diagonal lines to break down multi-digit multiplication into smaller, manageable steps.

An ancient multiplication technique, sometimes called 'doubling and halving,' involved decomposing one multiplicand into powers of two. Which civilization primarily used this method?

Ancient Egyptian multiplication is a systematic method that relies on decomposing one number into powers of two and repeatedly doubling the other number, then summing the results.

Which number is considered the multiplicative identity, meaning any number multiplied by it remains unchanged?

The Identity Property of Multiplication states that when any number is multiplied by 1, the product is that same number, hence 1 is known as the multiplicative identity.

Which result states that every integer greater than 1 is either prime or can be written as a product of primes in exactly one way, up to their order?

Insisting the factors be prime is what makes the result unique: 12 breaks up as both 2 times 6 and 3 times 4 if composite factors are allowed.

Logarithms were introduced in 1614 to simplify calculation. Which far easier operation do their tables let you substitute for laborious multi-digit multiplying?

The same identity works in reverse, turning division into subtraction.

Which Scottish mathematician built a set of numbered calculating rods for working out products and quotients, and named the technique rabdology?

The tables embedded in the rods reduce multiplying to a series of additions, and dividing to a series of subtractions.

Which hand-operated mechanical calculator uses sliding logarithmic scales to multiply, divide and take roots?

Sliding one scale along the other adds the logarithms of the two numbers, and the sum of the logarithms is the logarithm of the product.

Anatoly Karatsuba found the first method that beats the quadratic grade-school method for large numbers. In which year did he discover it?

It was published two years later. The Toom-Cook method of 1963 generalised it, and Schonhage-Strassen in 1971 went faster still for sufficiently large inputs.