Here we will certainly learn exactly how to discover the problems on ratios in simplest form. In order to express a ratio in the most basic form, we discover the HCF the the terms and divide every term by the HCF.

We know, a proportion must constantly be express in its lowest terms or simplest form. A proportion is said to be in the simplest kind if the first term or an initial quantity (antecedent) and also the second term or 2nd quantity (consequent) have no common factor various other than 1.

You are watching: Write the ratio in the simplest form 45:15

Find the ratio of each of the adhering to in most basic form:

**(i) 30 and also 15**

= 30 : 15

First we need to convert the given ratio into fraction,

= 30/15,

= 2/1

= 2 : 1

**(ii) 60 and 48**

**= 60 : 48**

**First we need to convert the offered ratio right into fraction,**

**= 60/48 (divide both the numerator and denominator by 12 since, the h.c.f. The 60 and also 48 is 12)**

**= 5/4**

**= 5 : 4**

**(iii) 8 kg and also 10 kg**

= 8 kg : 10 kg

= (8 kg)/(10 kg),

= 4/5

= 4 : 5

**Now, we will deal with different varieties of troubles on ratios in simplest type where both the amounts in various units. So, before finding the required ratio, we shall need to express both the quantities in the exact same units.**

**(iv) 3 kg to 2000 gm**

= 3 kg : 2000 gm

= (3 kg)/(2000 gm)

We know, 1 kg = 1000 gm, 3 kg = 3 × 1000 gm = 3000 gm,

= (3000 gm)/(2000 gm),

= 3/2

= 3 : 2

**(v) 750 gm to 2 kg 250 gm**

= 750 gm : 2 kg 250 gm

= (750 g)/(2 kg 250 gm)

We know, 1 kg = 1000 gm, 2 kg = 2 × 1000 gm = 2000 gm,

= (750 gm)/(2000 gm + 250 gm)

= 750/2250,

= 1/3

= 1 : 3

**(vi) 3 hours to 75 minutes**

**= 3 hrs : 75 minutes**

**= (3 hours)/(75 minutes) **

**We know, 1 hour = 60 minute, 3 hrs = 3 × 60 minutes = 180minutes,**

**= (180 minutes)/(75 minutes)**

**= 180/75**

**= 12/5**

**= 12 : 5**

**(vii) 2 hrs 15 minutes to 45 minutes**

= 2 hrs 15 minute : 45 minutes

= (2 hours 15 minutes)/(45 minutes)

We know, 1 hour = 60 minute, 2 hours = 2 × 60 minute = 120minutes,

= (120 + 15 minutes)/(45 minutes)

= 135/45

= 3/1

= 3 : 1

**(viii) 10 months and also 2 years**

= 10 month : 2 years

= (10 months)/(2 years)

We know, 1 year = 12 months, 2 years = 12 × 2 months = 24months,

= (10 months)/(24 months)

= 10/24

= 5/12

= 5 : 12

Thus, native the above problems ~ above ratios in simplest type wecan recognize that the two quantities deserve to be contrasted when they space of thesame kind. We have the right to compare the ages of two persons, however we cannot to compare theage that one human with, say, health or wealth of an additional person. Similarly,length and also width have the right to be contrasted becomes both the amounts are actions oflength. The measurements must additionally be in very same unit because that comparison.

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