proportion
In mathematics, a proportion is a statement that two ratios are equal
In mathematics, a proportion is a statement that two ratios are equal. It’s used to compare two or more quantities and express their relationship in terms of a ratio.
A proportion typically consists of four numbers arranged in two pairs, known as two ratios. These ratios are written in the form of fractions, where the numerators and denominators represent different quantities. The proportion states that the two ratios are equal.
A proportion can be represented symbolically as follows:
a/b = c/d
Here, a and d are called the extremes, while b and c are called the means. The product of the means (b and c) is equal to the product of the extremes (a and d).
Proportions are widely used in various fields, such as mathematics, science, finance, and everyday life situations. They are particularly useful for solving problems involving ratios and finding unknown values.
To solve a proportion, you can use a technique called cross multiplication. This involves multiplying the numerator of one ratio by the denominator of the other ratio and setting the products equal to each other. This allows you to find the value of the unknown variable.
For example, if you have the proportion:
2/5 = x/10
You can cross multiply:
2 * 10 = 5 * x
20 = 5x
Dividing both sides by 5 gives you the solution:
x = 4
Thus, the value of x that satisfies the proportion is 4.
Proportions are essential tools in many mathematical concepts, including solving for unknowns, understanding scale, and comparing different quantities. Understanding and using proportions allows you to make accurate comparisons and solve various real-life problems efficiently.
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