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 coprimes, 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
= \(\frac{5000 g}{500 g}\)
= \(\frac{5000}{500}\)
= \(\frac{10 × 500}{1 × 500}\)
= \(\frac{10}{1}\)
= 10 : 1
`2. Find the ratio of 40 min and 1\(\frac{1}{2}\) hr in the
simplest form.
Solution:
1\(\frac{1}{2}\) hr = (60 + 30) min = 90 min
Therefore, the given ratio = 40 min : 90 min
= \(\frac{40 min}{90 min}\)
= \(\frac{40}{90}\)
= \(\frac{10 × 4}{10 × 9}\)
= \(\frac{4}{9}\)
= 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
= \(\frac{325 cents}{925 cents}\)
= \(\frac{325}{925}\)
= \(\frac{25 × 13}{25 × 37}\)
= \(\frac{13}{37}\)
= 13 : 37.
4. Simplify the following ratios:
(i) 2\(\frac{2}{3}\) : 4\(\frac{1}{4}\)
(ii) 3.5 : 2\(\frac{1}{5}\)
(iii) 1\(\frac{1}{2}\) : \(\frac{2}{3}\) : 1\(\frac{1}{6}\)
Solution:
(i) 2\(\frac{2}{3}\) : 4\(\frac{1}{4}\)
= \(\frac{11}{3}\) : \(\frac{17}{4}\)
Now multiply each term by the L.C.M. of the denominators
= \(\frac{11}{3}\) × 12 : \(\frac{17}{4}\) × 12, [Since, L.C.M. of 3 and 4 = 12]
= 44 : 51
(ii) 3.5 : 2\(\frac{1}{5}\)
= \(\frac{35}{10}\) : \(\frac{11}{5}\)
Now multiply each term by the L.C.M. of the denominators
= \(\frac{35}{10}\) × 10 : \(\frac{11}{5}\) × 10, [Since, L.C.M. of 10 and 5 = 10]
= 35 : 22
(iii) 1\(\frac{1}{2}\) : \(\frac{2}{3}\) : 1\(\frac{1}{6}\)
= \(\frac{3}{2}\) : \(\frac{2}{3}\) : \(\frac{7}{6}\)
Now multiply each term by the L.C.M. of the denominators
= \(\frac{3}{2}\) × 6 : \(\frac{2}{3}\) × 6 : \(\frac{7}{6}\) × 6, [Since, L.C.M. of 2, 3 and 6 = 6]
= 9 : 4 : 7
● Ratio and proportion
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