Ratio and Proportion

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Ratio and Proportion

Ratio is a concept that you have probably encountered in other math classes. It is a comparison of sizes.


Ratio

The ratio of two numbers a and b is the fraction , usually expressed in reduced form. An alternative form involves a colon. The colon form is most frequently used when comparing three or more numbers to each other. See Table 1 .


TABLE 1Ratio Formats
RatioWritten Form
3 to 43/4 or 3 : 4
a to b, b ≠ 0 a/b or a : b
1 to 3 to 51 : 3 : 5

Example 1: A classroom has 25 boys and 15 girls. What is the ratio of boys to girls?





The ratio of boys to girls is 5 to 3, or 5/3, or 5 : 3.
Example 2: The ratio of two supplementary angles is 2 to 3. Find the measure of each angle.
  • The angles have measures of 72° and 108°.
  • 2 x to 3 x reduces to 2 to 3.
  • 2 x + 3 x = 180° (The sum of supplementary angles is 180°.)
  • 5 x = 180°
  • x = 36°
  • Then, 2 x = 2(36°) and 3 x = 3(36°).
  • So, 2 x = 72° and 3 x = 108°

The angles have measures of 72° and 108°.
Example 3: A triangle has angle measures of 40°, 50°, and 90°. In simplest form, what is the ratio of these angles to each other?
  • 40 : 50 : 90 = 4 : 5 : 9 (10 is a common divisor)

This means that:
  1. The ratio of the first to the second is 4 to 5.
  2. The ratio of the first to the third is 4 to 9.
  3. The ratio of the second to the third is 5 to 9.

Example 4: A 50-inch segment is divided into three parts whose lengths have the ratio 2 : 3 : 5. What is the length of the longest part?





The longest part has a measure of 25 inches.

Proportion

A proportion is an equation stating that two ratios are equal.





Means and extremes

The extremes are the terms in a proportion that are the farthest apart when the proportion is written in colon form ( a:b = c:d). In the foregoing, a and d are extremes. The means are the two terms closest to each other.






In the preceding proportion, the values a and d are called extremes of the proportion; the values b and c are called the means of the proportion.

Source-

CliffsNotes.com. Ratio and Proportion. 7 Feb 2013
< http://www.cliffsnotes.com/study_guide/topicArticleId-18851,articleId-18809.html>.

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