Proportion – Formula<\/h2>\n
Let us take, in proportion, the two ratios are x:y and m:n. The two terms m and n are called means or mean terms and x and y are called extremes or extreme terms.<\/p>\n
x : y :: m: n
\n\\(\\frac { x }{ y } \\) = \\(\\frac { m }{ n } \\)<\/p>\n
Example:
\nLet us consider the number of persons in a theater. Our first ratio of the number of girls to boys is 5:7 and that of the other is 3:5, then the proportion can be written as:
\n5 : 7 :: 3 : 5 or 5\/7 = 3\/5
\nHere, 5 & 5 are the extremes, while 7 & 3 are the means.
\nNote: The ratio value does not affect when the same non-zero number is multiplied or divided on each term.<\/p>\n
Important Properties of Proportion<\/h3>\n
The below are the important properties of proportions.<\/p>\n
- \n
- Addendo \u2013 If a : b = c : d, then a + c : b + d<\/li>\n
- Subtrahendo \u2013 If a : b = c : d, then a \u2013 c : b \u2013 d<\/li>\n
- Componendo \u2013 If a : b = c : d, then a + b : b = c+d : d<\/li>\n
- Dividendo \u2013 If a : b = c : d, then a \u2013 b : b = c \u2013 d : d<\/li>\n
- Invertendo \u2013 If a : b = c : d, then b : a = d : c<\/li>\n
- Alternendo \u2013 If a : b = c : d, then a : c = b: d<\/li>\n
- Componendo and dividendo \u2013 If a : b = c : d, then a + b : a \u2013 b = c + d : c \u2013 d<\/li>\n<\/ul>\n
Types of Proportions<\/h3>\n
The Proportions are classified into two types. They are<\/p>\n
- \n
- Direct Proportion<\/li>\n
- Inverse Proportion<\/li>\n<\/ul>\n
Direct Proportion:<\/strong> The Direct Proportion describes the direct relationship between two quantities. If one of the quantities increases, the other quantity increases and if one of the quantities decreases, the other quantity also decreases.
\nExample: If the speed of a vehicle increased, then it covers more distance in a fixed amount of time. It is denoted as y \u221d x.<\/p>\nInverse Proportion:<\/strong> The Inverse Proportion describes the indirect relationship between two quantities. If one quantity increases, the other quantity decreases, and If one quantity decreases the other quantity increases. It is denoted as y \u221d 1\/x.
\nExample: If a vehicle speed increases, then the result in converting a fixed distance in less time.<\/p>\n![\"Types](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Types-of-Proportions-300x183.jpg\")
<\/p>\nImportant Points on Proportion<\/h3>\n
Check out the important points that need to remember in the proportion concept.<\/p>\n
- \n
- Proportion is the comparison between two quantities.<\/li>\n
- The proportions are two types. One is direct proportions and inverse proportions.<\/li>\n
- Formula of proportion is \\(\\frac { x }{ y } \\) = \\(\\frac { m }{ n } \\)<\/li>\n
- The proportion is an equation.<\/li>\n<\/ul>\n
How to Solve Proportions?<\/h3>\n
Finding proportion is easy if the ratios are given. Follow the below procedure and find out the process to calculate proportions.
\n1. Multiply the first term with the last term: x x n
\n2. Multiply the second term with the third term: y x m
\n3. If the product of extreme terms is equal to the product of mean terms, then the ratios are proportional: x x n = y x m.<\/p>\nContinued Proportions<\/h3>\n
If we considered three quantities and the ratio of the first and second quantities is equal to the ratio between the second and the third quantities, then the three quantities are in Continued Proportions.<\/p>\n
Example:
\nLet us take the ratios a:b and c:d
\nIf a: b :: b: c, then we can say that a, b, c quantities are in continued proportion. Also, c is the third proportional of a and b.
\nb is called the mean proportional between a and C.
\nIf a, b, c are in continued proportion then b\u00b2 = ac or b = \u221aac.<\/p>\nProportion Examples with Answers<\/h3>\n
Example 1.<\/strong><\/p>\n
Determine if 4, 7, 8, 14 are in proportion?<\/p>\n
Solution:<\/strong>
\nGiven numbers are 4, 7, 8, 14.
\nFrom the given data, extreme terms are 4 and 13, mean terms are 7 and 6.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 4 \u00d7 14 = 56
\nProduct of mean terms = 7 \u00d7 8 = 56.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n56 = 56<\/p>\nTherefore, 4, 7, 8, 14 are in proportion.<\/p>\n
Example 2.<\/strong><\/p>\n
Check if 3, 6, 12 are in proportion.<\/p>\n
Solution:<\/strong>
\nGiven numbers are 3, 6, 12.
\nFrom the given data, 3 is the first term, 6 is the middle term, and 12 is the third term.
\nFind the Product of the first term and third term.
\nProduct of first and third term = 3 \u00d7 12 = 36
\nSquare of the middle terms = 6 \u00d7 6 = 36 = 3 \u00d7 12.
\nCompare the Product of the first and third term and Square of the middle terms.
\nThe Product of first and third term = Square of the middle terms
\n56 = 56<\/p>\nTherefore, 3, 6, 12 are in proportion, and 6 is called the mean proportional between 3 and 12.<\/p>\n
Example 3.<\/strong><\/p>\n
Find the fourth proportional to 3, 19, 21?<\/p>\n
Solution:<\/strong>
\nGiven numbers are 3, 19, 21.
\nTo find the fourth Proportional, let us assume the fourth proportional is x.
\nThen, 3: 19 :: 21: x
\nCompare the Product of extreme terms and Product of mean terms.
\n3x = 19 \u00d7 21
\n3x = 399
\nx = 399\/3
\nx = 133.<\/p>\nHence, the fourth proportional to 3, 19, 21 is 133.<\/p>\n
Example 4.<\/strong><\/p>\n
Find the third proportional to 4 and 8?<\/p>\n
Solution:<\/strong>
\nGiven numbers are 4 and 8.
\nLet the third proportional to 4 and 8 be x.
\nCompare the Product of the first and third term and Square of the middle terms.
\n4x = 8 \u00d7 8
\n4x = 64
\nx = 64\/4
\nx = 16<\/p>\nTherefore, the third proportional to 4 and 8 is 16.<\/p>\n
Example 5.<\/strong><\/p>\n
The ratio of income to expenditure is 3: 4. Find the savings if the expenditure is $24,000.<\/p>\n
Solution:<\/strong>
\nGiven that the ratio of income to expenditure is 3: 4.
\nTherefore, income = $ (3 \u00d7 24000)\/4 = $18000
\nSavings = Income – Expenditure = $24,000 – $18000 = $6000<\/p>\nThe savings are $6000 if the expenditure is $24,000.<\/p>\n
Example 6.<\/strong><\/p>\n
Find the mean proportional between 3 and 27?<\/p>\n
Solution:<\/strong>
\nGiven numbers are 3 and 27.
\nLet the mean proportional between 3 and 27 be x.
\nThen, x \u00d7 x = 3 \u00d7 27
\nx\u00b2 = 81
\nx = \u221a81
\nx = 9.<\/p>\nTherefore, the mean proportion between 3 and 27 is 9.<\/p>\n","protected":false},"excerpt":{"rendered":"
Proportion in Maths is an equation used to find that the two given ratios are equivalent to each other. Generally, we say that proportion defines that the equality of the two fractions of the ratios. If two sets of given numbers are increasing or decreasing in the same ratio with respect to each other, then … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":88307,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Proportions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/88302"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=88302"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/88302\/revisions"}],"predecessor-version":[{"id":91335,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/88302\/revisions\/91335"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/88307"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=88302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=88302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=88302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}