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Find the fourth proportional of 24, 8 and 9.
9
24
3
8
3
For four proportionals a, b, c, d where a:b :: c:d, simply calculate d = (b ├Ч c) / a. Here: (8 ├Ч 9) / 24 = 72 / 24 = 3.
Three numbers in proportion: a = 24, b = 8, c = 9
x=ab├ЧcтАЛ
For four proportionals a, b, c, d where a:b :: c:d, simply calculate d = (b ├Ч c) / a. Here: (8 ├Ч 9) / 24 = 72 / 24 = 3.
Many students mistake the order and calculate 24/8 = 9/x incorrectly as (249)/8 instead of (89)/24.
Define the Proportion
If x is the fourth proportional to 24, 8, and 9, then the numbers 24, 8, 9, and x are in proportion. This is written as 24 : 8 :: 9 : x.
24:8=9:x
Set up the equation
Convert the ratio into a fractional equation where the product of the means equals the product of the extremes: 24 * x = 8 * 9.
24x=72
Solve for x
Divide both sides by 24 to isolate x: x = 72 / 24.
x=2472тАЛ=3
C is correct because the fourth proportional of 24, 8, and 9 is calculated as (8 * 9) / 24, which equals 3.
This concept is foundational for solving variation problems in Physics, such as calculating resistance or gravitational forces where variables are directly or inversely proportional.
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