Answer:
We will learn how to express the ratio lowest term. The ratio of two or more quantities of the same kind and in the same units of measurement is a comparison obtained by dividing one quantity by the other. It is desirable to write a ratio in its lowest terms as, 15 : 10 = 3 : 2 (dividing both the term by 5). Then the ratio 3 : 2 is in its lowest term, 3 and 2 are co-primes, or their H.C.F. is 1.
1. Find the ratio of 5 kg : 500 g in the simplest from:
Solution:
5 kg = 5000 g
Therefore, the given ratio = 5 kg : 500 g
= 5000 g : 500 g
= 5000g500g
= 5000500
= 10×5001×500
= 101
= 10 : 1
2. Find the ratio of 40 min and 112 hr in the simplest form.
Solution:
112 hr = (60 + 30) min = 90 min
Therefore, the given ratio = 40 min : 90 min
= 40min90min
= 4090
= 10×410×9
= 49
= 4 : 9
3. Find the ratio of $ 3.25 : $ 9.25 in the simplest from:
Solution:
$ 3.25 = 325 cents and $ 9.25 = 925 cents
Therefore, the required ratio = 325 cents : 925 cents
= 325cents925cents
= 325925
= 25×1325×37
= 1337
= 13 : 37.
4. Simplify the following ratios:
(i) 223 : 414
(ii) 3.5 : 215
(iii) 112 : 23 : 116
Solution:
(i) 223 : 414
= 113 : 174
Now multiply each term by the L.C.M. of the denominators
= 113 × 12 : 174 × 12, [Since, L.C.M. of 3 and 4 = 12]
= 44 : 51
(ii) 3.5 : 215
= 3510 : 115
Now multiply each term by the L.C.M. of the denominators
= 3510 × 10 : 115 × 10, [Since, L.C.M. of 10 and 5 = 10]
= 35 : 22
(iii) 112 : 23 : 116
= 32 : 23 : 76
Now multiply each term by the L.C.M. of the denominators
= 32 × 6 : 23 × 6 : 76 × 6, [Since, L.C.M. of 2, 3 and 6 = 6]
= 9 : 4 : 7
