what is a proportion?
In mathematics, a proportion refers to an equation that states that two ratios are equal
In mathematics, a proportion refers to an equation that states that two ratios are equal. A ratio is the comparison of two quantities using division. Proportions are commonly used in various real-life situations, such as scaling up or down a recipe, solving problems involving rates, or calculating unknown values.
A proportion is written in the form of:
a/b = c/d,
where a, b, c, and d are numbers. The numbers a and d are called the extremes, while b and c are known as the means. In a proportion, the product of the means is equal to the product of the extremes.
Proportions can be used to solve unknown quantities. For example, if we have a proportion:
3/5 = x/10,
we can cross-multiply to find the value of x. Cross-multiplying means multiplying the numerator of one ratio by the denominator of the other ratio:
3 × 10 = 5 × x,
30 = 5x,
x = 6.
Therefore, the value of x in this proportion is 6.
Proportions are fundamental in many areas of mathematics, including algebra, geometry, and trigonometry. They provide a way to compare and relate quantities, helping us to solve problems and make predictions based on proportional relationships.
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