• RATIO
  • COMPARING RATIOS
  • PROPORTION
  • CHEKING PROPORTIONALITY
  • SOLVING SIMPLE PROPORTIONS

Ratio

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12.

We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.ATT00003.gif

Comparing Ratios

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.

Example:
Are the ratios 3 to 4 and 6:8 equal?

The ratios are equal if 3/4 = 6/8.

These are equal if their cross products are equal; that is, if 3 × 8 = 4 × 6. Since both of these products equal 24, the answer is yes, the ratios are equal

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Proportion

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.

3/4 = 6/8 is an example of a proportion.
When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.
Example:
Solve for n: 1/2 = n/4.

Using cross products we see that 2 × n = 1 × 4 =4, so 2 × n = 4. Dividing both sides by 2, n = 4 ÷ 2 so that n = 2.ATT00007.gif


Cheking proportionality
There is some terminology related to proportions that you may need to know. In the proportion:
a / b = c / d
a / b = c / d

...the values in the "b" and "c" positions are called the "means" of the proportion, while the values in the "a" and "d" positions are called the "extremes" of the proportion. A basic defining property of a proportion is that the product of the means is equal to the product of the extremes. In other words, given the proportional statement:
a / b = c / d
a / b = c / d

...you can conclude that ad = bc.
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Solving simple proportions
Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation. You'll probably start out by just solving proportions, like this:
    • Find the unknown value in the proportion: 2 : x = 3 : 9.
2 : x = 3 : 9
First, I convert the colon-based odds-notation ratios to fractional form:
.
2 / x = 3 / 9
2 / x = 3 / 9

Then I solve the proportion:
2 / x = 3 / 9
2 / x = 3 / 9


9(2) = x(3)

18 = 3x

6 = x
At last visit this page , look at the video where you can learn a lot about ratio and proportions and then do the quiz
http://www.bbc.co.uk/skillswise/topic/ratio-and-proportion

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