2 Express each of the following ratios in their lowest terms. (i) 39: 75 p p (in) 76 days : 1 year (iii) 15 weeks : 1 year (iv) 3 m : 90 cm (v) 650 g: 13 kg
Answers
i) 39 : 75
= 39/75
= 13/25
= 13 : 25
ii) 76 days : 1 year
= 76 days : 366 days (leap year)
= 76/366
= 38/183
= 38 days : 183 days
iii) 15 weeks : 1 year
= 105 days : 365 days
= 105/365
= 21/73
21 days : 73 days
iv) 3 m : 90 cm
= 300 cm : 90 cm
= 300/90
= 10/3
= 10 cm : 3cm
v) 650 g : 13 kg
= 650 g : 13000 g
= 650/13000
= 1/20
= 1 g : 20 g
Answer:
Lowest term of (i) 39 /75 ( i i ) 76 / 365 ( iii ) 15 / 52 ( 1 v ) 10 / 3 (v) 1 /20
Step-by-step explanation:
(i) 39 : 75
= 39 /75
= ( 39 ÷ 3 ) / ( 75 ÷ 3)
= 13 / 25
As there is no common factor between 13 and 25 so it is in the lowest term.
( ii ) 76 days : 1 yr.
Since days and yr are two different units .so we convert yr into days
1 yr = 365 days
76 : 365
As there is no common factor between 76 and 365 .so it is in the lowest term.
(iii) 15 weeks : 1yr.
Week and yr. are 2 different units so we convert yr into week
1 yr = 52 weeks
15 weeks : 52 weeks= 15 / 52
As there is no common factor between 15 and 52 so it is in the lowest term.
(iv) 3m. :90 cm.
As m. and cm. are two different units so we convert m. into cm.
1 m. =100 cm.
3 m. =300 cm.
3 m. : 90 cm = 300 : 90
= (300 ÷30) / (90 ÷ 30)
=10 / 3
As there is no common factor so it is in the lowest form.
(v) 650 gm. : 13 kg.
1 kg. = 1000 gm.
13 kg. = 13000 gm.
650 gm : 13000 gm = ( 650 ÷130 ) / (13000 ÷ 130 )
= 5 /100
= ( 5 ÷ 5 ) / ( 100 ÷ 5)
= 1 ; 20