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Definition of Algorithm in Mathematics

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Updated December 12, 2017

**Definition: **When the term algorithm is used in math, it typically refers to a set of steps used to solve a mathematical computation. A step by step procedure is used in long division. A simple question like 73 divided by 3 would have the following algorithm:

How many times does 3 go into 7?

The answer is 2

How many are left over? 1

Put the 1(ten) in front of the 3.

How many times does 3 go into 13?

The answer is 4 with a remainder of one.

And of course the anser becomes 24 with a remainder of 1.

The step by step procedure used to do the long division computation is considered a long division algorithm.

**Examples: **FOIL is another example of an algorithm used in algebra. The steps in FOIL are: First outside, inside last. This algorithm is useful for multiplying polynomials. BEDMAS is another useful set of steps and is also considered a formula. BEDMAS: Brackets, Exponents, Division, Multiplication, Addition and Subtraction. This refers to an order of operations.

Algorithms are about finding efficient ways to do math. A colleague and friend of mine used to always say that 'mathematicians' are lazy so they are always looking for short cuts. Hence we use the algorithms. If you think about multiplication, it's really adding the same number that many more times. Who wants to keep adding a number over and over again? The algorithm is usually the most efficient (not always) way to do math.

When watching your students do their math, a great question to pose to them is "Can you think of a quicker way to do that?" We always want to push our students to think about efficient strategies in math.