Multiple (mathematics)

In mathematics, a multiple is a special kind of number you get when you multiply any quantity by a whole number, called an integer. For example, if you have the number 3 and multiply it by 4, you get 12. In this case, 12 is a multiple of 3, and 4 is called the multiplier.

When two numbers are both whole numbers, and one is a multiple of the other, the smaller number is called a divisor of the larger one. We also say that the smaller number divides the larger one.

The word "multiple" can also be used in other areas of math. For example, in algebra, a polynomial (which is an expression with letters and numbers) can be a multiple of another polynomial if you can multiply the second polynomial by a third one to get the first.

Examples

Some numbers are multiples of 7, like 14, 49, -21, and 0. These can be made by multiplying 7 by another whole number. For example, 14 is 7 times 2, 49 is 7 times 7, -21 is 7 times -3, and 0 is 7 times 0.

Other numbers, like 3 and -6, are not multiples of 7. This is because when you try to write them as 7 multiplied by another number, that other number is not a whole number. For 3, you would need to multiply 7 by 3/7, which is not a whole number. The same goes for -6, where you would need to multiply 7 by -6/7, also not a whole number.

Properties

In math, a multiple is when you multiply a number by another whole number. For example, zero is a multiple of every number because zero times any number equals zero. Also, any whole number multiplied by one stays the same, so every number is a multiple of itself. If you have two numbers that are multiples of another number, adding or subtracting those two numbers will also give you a multiple of that same number.

Submultiple

In some books, we say that "a is a submultiple of b" when a is one part of b divided by a number (like b divided by n). This idea is also used with measuring units. For example, a millimetre is one-thousandth of a metre, and one inch can be thought of as one-twelfth of a foot or one-thirty-sixth of a yard.