Proportion
Proportion is a mathematical concept that compares two ratios or quantities to determine if they are equivalent
Proportion is a mathematical concept that compares two ratios or quantities to determine if they are equivalent. In a proportion, the relation between the quantities remains the same even when the values may change.
A proportion is usually written in the form of two fractions or ratios separated by an equal sign. For example, the proportion 3/4 = 6/8 states that the ratio of 3 to 4 is the same as the ratio of 6 to 8, which shows that these two ratios are equivalent.
When working with proportions, there are various ways to solve them. One common method is cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction, and then setting the two products equal to each other. The resulting equation can be solved to find the unknown value.
Let’s work through an example to illustrate the use of proportions:
Problem: Solve the proportion 2/5 = x/15
Solution:
To solve this proportion, we can use the cross-multiplication method.
First, we cross-multiply by multiplying the numerator of one fraction by the denominator of the other.
(2)(15) = (5)(x)
30 = 5x
Next, we solve the equation by isolating the variable x. In this case, we divide both sides of the equation by 5.
30/5 = x
6 = x
So, the value of x that satisfies the proportion is 6.
In conclusion, proportions are a useful tool in mathematics for comparing ratios and determining equivalence. By using cross-multiplication or other methods, we can solve proportions to find unknown values.
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