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

● **Ratio and proportion**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of 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.