Page 203 - 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 __________

Property 2: Ratio is determined between the same kinds of quantities, which means they have the
same units.

For example: If there is 10 metre blue ribbon and 19 metre red ribbon, then the ratio of the length
10m 10
of blue ribbon to the length of red ribbon = = = 10 : 19 as both are in the same unit.
19m 19
Hence, we can say that the ratio of two quantities is just a number, and it has no unit.
Property 3: If each term of a ratio is multiplied or divided by the same non-zero number, the ratio remains
the same.
For example:
×
3 32 6
(a) 3 : 4 = = = . Here, 3 : 4 = 6 : 8
4 42 8
×
÷
16 16 4 4
(b) 16 : 20 = = = . Here, 16 : 20 = 4 : 5
20 20 4 5
÷
Example 1: Find the ratio of the following:
( a) 18 m to 56 m (b) 15 kg to 48 kg (c) 240 mL to 500 mL

( d) 20 min to 2 hr (e) 25 p to `10 (f) 3 kg to 1800 g
18m 18 9
Solution: (a) 18 m to 56 m = = = = 9 : 28
56m 56 28

15kg 15 5
( b) 15 kg to 48 kg = = = = 5 : 16
48kg 48 16
240mL 240 12
( c) 240 mL to 500 mL = = = = 12 : 25
500mL 500 25

20min 20min 20 1
( d) 20 min to 2 hr = = = = = 1 : 6
2hr 260min 120 6 Remember
×
If the quantities are in
25p 25p 25 1
( e) 25 p to `10 = = = = = 1 : 40 different units, first convert
×
` 10 10 100p 1000 40 them into the same units
3kg 3 1000g 3000 5 and then find the ratio
×
( f) 3 kg to 1800 g = = = = = 5 : 3 between them.
1800g 1800g 1800 3
Simplest Form of Ratio

A ratio is said to be in the simplest form when both of its terms do not have any common factor
except 1. To convert a ratio in its simplest form, we divide both the terms (antecedent and
consequent) by the HCF of these terms.
For example: 8 : 16 can be written in the simplest form as 1 : 2. Prime factorization of 36

Example 2: Reduce the ratio 36 : 45 into its simplest form. = 2 × 2 × 3 × 3
Prime factorization of 45
Solution: To reduce the given ratio in its simplest form, we divide the = 3 × 3 × 5
terms of the given ratio, i.e., 36 and 45, by their HCF. H.C.F. of 36 and 45
HCF of 36 and 45 is 9. = 3 × 3 = 9

201 Ratio and Proportion