Q:

# What is the definition of extremes in math?

A:

When solving proportions in math, the outer terms in the calculation are the extremes, and the middle terms are called the means. When setting the proportion equation a/b = c/d, the a and the d figures are the extremes. Cross multiplication to solve the equation yields a x d = b x c, and division allows for solving to identify the quantity of the variable.

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Credit: Erick Kaukomieli CC-BY-SA 2.0

The following word problem gives a step-by-step explanation for solving this type of proportion.

Two picnic tables are of different sizes but have proportionate dimensions. The larger table is 15 feet wide by 10 feet long, and the smaller table is 9 feet wide. What is the length of the smaller table?

The proportion sets up as follows: 15/10 = 9/x. In this problem, 15 and x are the extremes, and 9 and 10 are the means. Cross multiplying yields 15x = 90, and dividing both sides by 15 yields an answer of x = 6. Each table has a proportion of 2:3 when it comes to length:width, and the smaller table's dimensions are 3/5 those of the larger table.

Understanding how extremes and means work when solving proportion equations is one of the most important concepts to master in the early phases of algebra.

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