Ratio in Lowest Term

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

                                          = \(\frac{5000 g}{500 g}\)

                                          = \(\frac{5000}{500}\)

                                          = \(\frac{10 × 500}{1 × 500}\)

                                          = \(\frac{10}{1}\)

                                          = 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











10th Grade Math

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