What is 1:1 in maths?

The meaning of "1:1" in maths depends on the context. It can refer to a ratio, a one-to-one function, or a scaled model.

Ratios

A 1:1 ratio means that there is an equal amount of two things being compared. For example, if a recipe calls for a 1:1 ratio of flour to sugar, it means you need the same amount of flour and sugar.
- Example: If you need 1 cup of flour, you also need 1 cup of sugar.
- Another example: If you need 1 gram of salt, you will also need 1 gram of pepper.

In the context of functions, a "1:1" or one-to-one function (also called an injective function) means that each element of the range is associated with exactly one element of the domain. In simpler terms, if f(x) = f(y), then x = y. This means no two different inputs produce the same output.
- Example: The function f(x) = x + 1 is one-to-one. If x and y are different, x+1 and y+1 will be different.
- Non-example: The function f(x) = x² is not one-to-one because f(2) = 4 and f(-2) = 4. Two different inputs (2 and -2) produce the same output (4).

A 1:1 scale means that the model is the same size as the real object. For instance, a 1:1 scale model of a toy car would be the actual size of the toy car.
- Example: If a map is drawn to a 1:1 scale, then one centimeter on the map represents one centimeter in reality.

Based on the provided reference, the expression "1+1" is equal to 2 in ordinary arithmetic. While not directly related to "1:1," it highlights basic mathematical operations.
- Example: The expression 1+1 mathematically evaluates to 2.