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
From Ratio in Lowest Term to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.