In mathematics, a ratio is a relationship between two numbers of the same kind (e.g., objects, persons, students, spoonfuls, units of whatever identical dimension), expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two that explicitly indicates how many times the first number contains the second (not necessarily an integer). In layman's terms a ratio represents, for every amount of one thing, how much there is of another thing. For example, supposing one has 8 oranges and 6 lemons in a bowl of fruit, the ratio of oranges to lemons would be 4:3 (which is equivalent to 8:6) while the ratio of lemons to oranges would be 3:4. Additionally, the ratio of oranges to the total amount of fruit is 4:7 (equivalent to 8:14). The 4:7 ratio can be further converted to a fraction of 4/7 to represent how much of the fruit is oranges. The ratio of numbers A and B can be expressed as: - the ratio of A to B
- A is to B (often followed by "as ...")
- A:B
- A fraction (rational number) that is the quotient A divided by B: A/B
The numbers A and B are sometimes called terms with A being the antecedent and B being the consequent. The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. This latter form, when spoken or written in the English language, is often expressed as A, B, C and D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means. The equality of three or more proportions is called a continued proportion. Ratios are sometimes used with three or more terms. The ratio of the dimensions of a "two by four" that is ten inches long is 2:4:10. A good concrete mix is sometimes quoted as 1:2:4 for the ratio of cement to sand to gravel. For a mixture of 4/1 cement to water, it could be said that the ratio of cement to water is 4:1, that there is 4 times as much cement as water, or that there is a quarter (1/4) as much water as cement.. Older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height; modern widescreen TVs have a 16:9 aspect ratio. |