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 Amsco Integrated Algebra I: Ratio
This is a free lesson from our course in Amsco's Integrated Algebra
This lesson covers concepts and explanation of ratio, equivalent ratio and continued ratio. A ratio is comparison of two numbers or two similar quantities by division is the quotient obtained when the first number is divided by the second non-zero number. Ratios are written with: symbol. For example, ratio of 6 to 3 can be written as 6 ÷ 3, 6/3, 6:3 = 2. Similarly the ratio of 3 to 6 is 3 ÷ 6, 3/6, 3: 6= 1/2. Equivalent ratio is the ratio obtained when we apply multiplication property of 1 to a fraction. For example: equivalent ratios of 3/1 are (3*2)/(1*2)=6/2.In general it may be expressed as (3*n)/(1*n), where n is the multiplying number. (More text below video...)
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(Continued from above) Continued ratio is comparison of three or more quantities in a definite order. In general, the ratio of the numbers a, b and c (b!=0,c!=0) is a:b:c. E.g. the ratio of the measures of the length, width, and height (in that order) of the rectangular solid is 75 : 60 : 45 or, in its simplest form… 5 : 4 : 3.
In a simpler way it can be illustrated like, say for example: The ratio of Apples to Oranges is 5 to 7. If there are 156 fruits total, how many Apples are there? To find the solution to this problem, write down the information given and inferred.
A = 5 O = 7 T = 12
With this information, there are three different ratios you can write.
A/O = 5/7
A/T = 5/12
O/T = 7/12
The solution is to find about Apples and fruits total, so we will use the second ratio and replace the variable T with 156. It gives,
A/156 = 5/12
12 x A = 5 x 156
A = 65
Apples are 65, as the final answer.
Remember it:
• since a ratio is only a comparison or relation between quantities, it is an abstract number. E.g. ratio of 8 feet to 4 feet is only 2, not 2 feet.
• ratios can be written as fractions and they have all the properties of fractions (as stated in earlier learning of lessons)
• precisely the ratio of 6 to 3 should be stated as 2 to 1, but in commonly used language, the expression of ratios is called 2.
• where two quantities cannot be expressed with the same unit, they cannot have a ratio between them.

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