Continued Proportion

Continued proportion : Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion.
Thus, if a, b and c are in continued-proportion, then
a,b,b,c are in proportion, that means
a : b : : b : c
⇒ Product of extremes = Product of means
⇒ a x c = b x b
⇒ a x c = b²
Continued-proportion is also known as mean proportional .
If ‘b’ is a mean proportional between a and c then b² = ac.

Examples :
1) Find the mean proportional between 9 and 25.
Solution :
Let x be the mean proportional between 9 and 25.
⇒ x² = 9 x 25
⇒ x² = 225
⇒ x = 15
Hence, the mean proportional between 9 and 25 is 15.
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2) If 3, x , 12 are in continued-proportion, find the value of x.
Solution :
Since 3,x,12 are in continued-proportion,
3,x,x,12 are in proportion.
Product of extremes = Product of means
⇒ 3 x 12 = x . x
⇒ 36 = x²
⇒ x = 6.
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3) If 40, x, x, 40 are in proportion, then find the value of x.
Solution :
Product of means = product of extremes
x. x = 40 x 40
⇒ x² = 1600
⇒ x = 40
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4) If we divide 20 between Jacob and Ariel in the ratio 3 : 2, how much will each of them get? what number is a mean proportional between those parts?
Solution :
Sum of the two terms of the ratio (3 : 2) =3 + 2 = 5
Jacob's share = (3/5) x 20 = 12
Ariel's share =(2/5) x 20 = 8
Mean proportion of 12 and 8 is √(12 x 8)
⇒ √(96)
⇒ √(16 x 6)
⇒ 4√6

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Ratio - Proportion

• Ratio and Proportion
• Ratio in the simplest form
• Comparison of ratios
• Equivalent ratios
• Proportion
• Continued Proportion

From continued-proportion to number system

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