Table of Contents
- Comparing Ratios
- Summary
- What’s Next?
In the previous segment, we had looked at the comparison of Ratios. In this segment of the
chapter ‘Comparing Quantities’, we will see how to compare ratios.
Comparing Ratios
Consider two ratios a : b and c : d. That is, ? ??? ?
? ?
To compare these two ratios we will consider the products
- ad (the product of the numerator of the first ratio and the denominator of the second ratio)
- bc (the product of the denominator of the first ratio and the numerator of the second ratio)
Then compare these two products and determine the comparison of the ratios using the following concept:
- If ??< ??, then a : b < c : d.
- If ??= ??, then a : b = c : d.
- If ??> ??, then a : b > c : d.
Let us understand this with the help of some examples.
(i) 3 : 5 and 7 : 2.
To compare this, let us consider the products 3 x 2 = 6 and 7 x 5 = 35.
Here, 6 < 5.
That is, (3 x 2) < (7 x 5).
Hence, 3 : 5 < 7 : 2.
(ii) 2 : 15 and 10 : 99.
To compare this, let us consider the products 2 x 99 = 198 and 10 x 15 = 150.
Here, 198 > 150.
