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The product of means and extremes refers to a property in proportions. If two ratios (a/b = c/d) are equal, then the product of the means (b and c) is equal to the product of the extremes (a and d), expressed as (b \cdot c = a \cdot d). This relationship is often used in solving problems involving proportions, ensuring that the cross-multiplication yields equivalent results.
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What is the definition of means and extremes?
In mathematics, particularly in the context of proportions, the terms "means" and "extremes" refer to the four terms in a proportion ( \frac{a}{b} = \frac{c}{d} ). In this case, ( a ) and ( d ) are called the extremes, while ( b ) and ( c ) are the means. The relationship signifies that the product of the means equals the product of the extremes, or ( a \times d = b \times c ). This concept is fundamental in solving problems involving ratios and proportions.
What is the mathematical term the product of the mean equals the product of the extremes?
: The product of the means is equal to the product of the extremes. When you cross multiply to show 2 fractions are equivalent. Ex a/c =b/d so cross multiplying would show a x d = c x b c x b are the means a x d are the extremes Their products are equal in a proportion or equivalent fractions that is the answer and it is correct
What is the product of the extremes?
The product of the extremes refers to a concept in proportions, where it involves the multiplication of the two outer terms in a ratio. For example, in the proportion ( \frac{a}{b} = \frac{c}{d} ), the product of the extremes would be ( a \times d ). This is equal to the product of the means, ( b \times c ), confirming the equality of the two ratios. This relationship is fundamental in solving problems involving proportions.
What is the cross product method?
If a is to b as c is to d, a x d = b x c. The product of the means (b & c) equals the product of the extremes (a & d).
Why does cross multiplying with fractions work?
When cross multiplying, finding the product of the means and extremes, you are technically getting a common denominator that reduces out.
What is the product of the extremes and the means called?
i don't know and i want to know too!
What is the definition of means and extremes?
In mathematics, particularly in the context of proportions, the terms "means" and "extremes" refer to the four terms in a proportion ( \frac{a}{b} = \frac{c}{d} ). In this case, ( a ) and ( d ) are called the extremes, while ( b ) and ( c ) are the means. The relationship signifies that the product of the means equals the product of the extremes, or ( a \times d = b \times c ). This concept is fundamental in solving problems involving ratios and proportions.
What is the product of the numerator of one ratio and the denominator of the other ratio called in a proportion?
The numerator of the second ratio and the denominator of the first ratio are called the means, and the numerator of the first ratio and the denominator of the second ratio are called the extremes. The product of the means equals the product of the extremes.
What is the mathematical term the product of the mean equals the product of the extremes?
: The product of the means is equal to the product of the extremes. When you cross multiply to show 2 fractions are equivalent. Ex a/c =b/d so cross multiplying would show a x d = c x b c x b are the means a x d are the extremes Their products are equal in a proportion or equivalent fractions that is the answer and it is correct
What is the product of the extremes?
The product of the extremes refers to a concept in proportions, where it involves the multiplication of the two outer terms in a ratio. For example, in the proportion ( \frac{a}{b} = \frac{c}{d} ), the product of the extremes would be ( a \times d ). This is equal to the product of the means, ( b \times c ), confirming the equality of the two ratios. This relationship is fundamental in solving problems involving proportions.
What is the cross product method?
If a is to b as c is to d, a x d = b x c. The product of the means (b & c) equals the product of the extremes (a & d).
Why does cross multiplying with fractions work?
When cross multiplying, finding the product of the means and extremes, you are technically getting a common denominator that reduces out.
How do you write a proportion?
One standard way is it use colons , For example 7:14::6:12 read as 7 is to 14 as 6 is to 12. The number in the middle are called the means; those on either end are called the extremes. In a correct proportion, the product of the means equals the product of the extremes. In the example, note that 7 times 12 = 14 times 6.
What is the Means-Extremes Product Property of Proportions?
The means-extreme property of proportions is the method that allows you to cross multiply an equation to find the answer. An example would be, if a/b = c/d then ad = bc.
If the product of the extremes is 8then the geometric mean is?
The geometric mean of two numbers is calculated as the square root of their product. If the product of the extremes is 8, then the geometric mean is the square root of 8, which simplifies to ( \sqrt{8} = 2\sqrt{2} ) or approximately 2.83.
If the product of the extremes is 8 then the geometric mean is?
It is sqrt(8) = 2*sqrt(2) = 2.823, approx.
How many inches are in 3 over 4 of a yard?
one yard is 36 inches, so 1/4 of a yard is 36/4=9. So 3/4 of a yard would be 9x3, or 27 inches A common method of solving problems like this is through the principle that for equal fractions, the product of the means is equal to the product of the extremes. 3 over 4 is equal to what over 36. Using the variable "x" for what, this can be written as 3/4 = x/36. The product of the means (4 & x) is equal to the product of the extremes ( 3 & 36), or 4x= 3 times 36 4x= 108 so divide both sides of the equation by 4, gives us x=27
