Page 209 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\09_Chapter\09_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

So, it is clear that 3 : 5 = 360 : 600, and we say that ratio 3 : 5 is proportional to the ratio 360 : 600.

Thus, in a proportion two ratios are set equal to each other.
The equality of two ratios is called proportion, and consequently, their Remember
terms are said to be in proportion. It is denoted by the symbol ‘: :’ or The symbol (‘: :’) has the
‘=’ to equate the ratios. same meaning as (‘=’), that
Here, the quantities 3, 5, 360, and 600 are in proportion. means to equate the two
ratios.
Thus, 3 : 5 : : 360 : 600
In general, four quantities a, b, c, and d are said to be in proportion, if a : b = c : d or a : b : : c : d

And we read it as (a is to b) as (c is to d). a c means
Here, a, b, c, and d are respectively known as first, second, third, b = d a : b = c : d
and fourth terms of the proportion.
The first and fourth terms, that are a and d, are called extreme means extremes extremes
terms and the second and third terms, that are b and c, are called means or middle terms.
In all, we can say that, the four terms a, b, c, and d are in proportion, if: Product of Product of
Product of extreme terms = Product of middle terms a c extremes means

that is, a × d = b × c b = d → a × d = b × c
Example 12: Are 40 kg : 48 kg and `250 : `300 in proportion? If a × d ≠ b × c, then they are
40 kg 5 not in proportion.
Solution: 40 kg : 48 kg = = = 5 : 6
48 kg 6
`250 5 Remember
`250 : `300 = = = 5 : 6 In proportion it is not always necessary
`300 6
that all the four quantities are of the same
Clearly, 250 : 300 = 40 : 48 kind. It means that the first two quantities

Hence, the ratios 40 kg : 48 kg and `250 : `300 are in can be of the same kind and the other two
proportion, i.e., 40 kg : 48 kg : : `250 : `300. quantities can be of different kind.

Example 13: Verify that the ‘product of extremes = the product of means’ for the given ratios. Also,
check they are in proportion or not.
Product of means
( a) 6 : 9 and 16 : 24 (b) 18:20 and 45:36 = 9 × 16 = 144

Solution: (a) 6 : 9 and 16 : 24 6 : 9 : : 16 : 24
Product of extremes = 6 × 24 = 144
Product of extremes
Product of means = 9 × 16 = 144 = 6 × 24 = 144

Clearly, product of extremes = product of means
Hence, 6 : 9 and 16 : 24 are in proportion, that is, 6 : 9 : : 16 : 24.

( b) 18:20 and 45:36
Product of means
Product of extremes = 18 × 36 = 648 = 20 × 45 = 900
Product of means = 20 × 45 = 900 18 : 20 : : 45 : 36

648 ≠ 9 Product of extremes
Clearly, product of extremes ≠ product of means = 18 × 36 = 648
Hence, 18:20 and 45:36 are not in proportion.

207 Ratio and Proportion