Multiplication and division

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Just like addition and subtraction, multiplication ([math]x[/math], [math].[/math]) and division (÷, [math]/[/math]) are opposites of each other. Multiplying by a number and then dividing by the same number gets us back to the start again:

  • [math]a[/math] × [math]b / b = a[/math]
  • [math]5[/math] x [math]4 / 4 = 5[/math]

Sometimes you will see a multiplication of letters as a dot or without any symbol. Don’t worry, its exactly the same thing. Mathematicians are efficient and like to write things in the shortest, neatest way possible.

  • [math]abc = a [/math]×[math] b [/math]×[math] c[/math]
  • [math]a [/math]·[math] b [/math]·[math] c = a [/math]×[math] b [/math]×[math] c[/math]

It is usually neater to write known numbers to the left, and letters to the right. So although 4[math]x[/math] and [math]x[/math]4 are the same thing, it looks better to write 4[math]x[/math]. In this case, the “4” is a constant that is referred to as the coefficient of x.

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Extension exercise

Commutativity for Multiplication

The fact that [math]ab = ba[/math] is known as the commutative property of multiplication. Therefore, both addition and multiplication are described as commutative operations.

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