Basic Concepts in Proportion – Part 2

Table of Contents

• Continued Proportion
• Summary
• What’s Next?

In the previous segment of Class 6 Maths, we learnt about some basic concepts in proportion.

Here, let us learn about Continued proportion.

What is Continued proportion?

Consider two ratios a : b and b : c, such that ? = ?.Thus, a : b : : b : c.

? ?

In such cases, where two ratios are equal such that the denominator of the first ratio is equal to the numerator of the second ratio, the proportion is known as Continued proportion.

Here we say a, b, and c are in continued proportion.

The terms a and c are at the extreme ends and hence, known as the extremes. The term b is in the middle and hence, known as the mean proportional.

When a, b, and c are in continued proportion, ? × ? = ?².

That is, the ??????? ?? ?ℎ? ???????? = (???? ????????????)².

For example, consider 2 ??? 8 .

8 32

Here, 2 = 8 . Thus, 2, 8, and 32 are in continued proportion.

8 32

2 and 32 are the extremes while 8 is the mean proportional.

Product of the extremes = 2 x 32 = 64

(???? ????????????)² = 8² = 8 × 8 = 64

Thus, the ??????? ?? ?ℎ? ???????? = (???? ????????????)²