How to make a proportion?
From the point of view of mathematics, the proportion is the equality of two relations. Interdependence is characteristic of all parts of the proportion, as well as their constant result. You can understand how to make a proportion by reading the properties and the formula of proportion. To understand the principle of solving the proportion, it is sufficient to consider one example. Only directly solving the proportions, you can easily and quickly learn these skills. And this article will help the reader in this.
Proportion properties and formula
- Reversal of proportion. In the case when the given equality looks like 1a: 2b = 3c: 4d, write 2b: 1a = 4d: 3c. (Moreover, 1a, 2b, 3c, and 4d are primes other than 0).
- The multiplication of the given members of the proportions crosswise. In letter form, it looks like this: 1a: 2b = 3c: 4d, and the record 1a4d = 2b3c will be equivalent to it. Thus, the product of the extreme parts of any proportion (the numbers on the edges of equality) is always equal to the product of the middle parts (numbers located in the middle of the equality).
- In drawing up a proportion, its property, such as a permutation of the extreme and middle terms, can be useful.Equality formula 1a: 2b = 3c: 4d, can be displayed with such options:
- 1a: 3c = 2b: 4d (when the mean proportions are swapped).
- 4d: 2b = 3c: 1a (when rearranging the extreme terms of proportion).
- Perfectly helps in solving the proportion of its property of increasing and decreasing. When 1a: 2b = 3c: 4d, write:
- (1a + 2b): 2b = (3c + 4d): 4d (equality in terms of increasing proportion).
- (1a - 2b): 2b = (3c - 4d): 4d (equality to reduce the proportion).
- You can make a proportion by addition and subtraction. When the proportion is written as 1a: 2b = 3c: 4d, then:
- (1a + 3c): (2b + 4d) = 1a: 2b = 3c: 4d (the proportion is composed by addition).
- (1a - 3c): (2b - 4d) = 1a: 2b = 3c: 4d (the proportion is composed by subtraction).
- Also, when solving a proportion containing fractional or large numbers, you can divide or multiply both of its members by the same number. For example, the component parts of the proportion 70: 40 = 320: 60, you can write this: 10 * (7: 4 = 32: 6).
- The solution to proportions with percentages is as follows. For example, write, 30 = 100%, 12 = x. Now it is necessary to multiply the middle terms (12 * 100) and divide by the known extreme (30). Thus, the answer is obtained: x = 40%. In a similar way, you can, if necessary, multiply the known extreme members and divide them by a given average number, obtaining the desired result.
If you are interested in a specific formula of proportion, then in the simplest and most widespread form the proportion is such an equation (formula): a / b = c / d, in it a, b, c and d are non-zero four numbers.
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