KHAN ACADEMY INTRODUCTION TO RATIOS VIDEO
In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.[1] For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Thus, a ratio can be a fraction as opposed to a whole number. Also, in this example the ratio of lemons to oranges is 6:8 (or 3:4), and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).
The numbers compared in a ratio can be any quantities of a comparable kind, such as objects, persons, lengths, or spoonfuls. A ratio is written "a to b" or a:b, or sometimes expressed arithmetically as a quotient of the two.[2]When the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units. But in many applications, the word ratio is often used instead for this more general notion as well.[3]
The ratio of numbers A and B can be expressed as:[4]
- the ratio of A to B
- A is to B (followed by "as C is to D")
- A:B
- A fraction that is the quotient: A divided by B:
, which can be expressed as either a simple or a decimal fraction.[5]
The numbers A and B are sometimes called terms with A being the antecedent and B being the consequent.[6]
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 is to B as C is to D.
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.[7]
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.[8]
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.
