Question

Write the ratio of first quantity to second quantity in the reduced form.
(i)1024 MB, 1.2GB [(1024 MB = 1GB)]
(ii)17 Rupees, 25 Rupees 60 paise
(iii)5 dozen, 120 units

Answer 1

Hint: In this question we have to compare one value to another value respectively taking care of the units that must be the same. As in (i) part you can convert MB to GB (ii) part you have to convert either in rupees or in paise. And in the (iii) part you convert a dozen into units.
Formula Used: \[1024MB = 1GB\] , \[1Rs = 100paise\] , \[1dozen = 12units\]

Complete step-by-step answer:
 So, let us begin with the question:
(i)1024 MB,1.2GB
Firstly, convert 1024 MB to GB:
As, \[1024MB = 1GB\]
We will multiply \[1024MB = 1 * 1GB\]
\[ \Rightarrow 1GB\]
Units get cancelled out while calculating ratio.
\[Ratio = \dfrac{1}{{1.2}}\]
\[ \Rightarrow \dfrac{{10}}{{12}}\]
Now, let’s divide numerator and denominator with 2.
After dividing we get,
\[ \Rightarrow \dfrac{5}{6}\]
Now, 5 is not divisible by 6. Means we have got our ratio that is \[5:6\] .
\[Ratio = 5:6\]

(ii)17rupees, 25 rupees 60 paise
Firstly, convert 25 rupees 60 paise into rupees:
As, \[1paise = \dfrac{1}{{100}}rupees\]
\[60paise = \dfrac{{60}}{{100}}rupees\]
Cutting zeros from numerator and denominator.
\[ \Rightarrow 0.6rupees\]
So, we get \[25.6rupees\]
\[Ratio = \dfrac{{17}}{{25.6}}\]
\[ \Rightarrow \dfrac{{170}}{{256}}\]
Now, let’s divide numerator and denominator with 2.
After dividing we get,
\[ \Rightarrow \dfrac{{85}}{{128}}\]
Now, 85 is not divisible by 128. Means we have got our ratio that is \[85:128\] .
\[Ratio = 85:128\]

(iii)5dozen, 120units
Firstly convert dozen to units:
As , \[1dozen = 12units\]
We will multiply 5dozen with 100 \[\therefore 5dozen = 5 * 12units\]
\[ \Rightarrow 60units\]
Now both 5 dozen and 120 units are in the form of units. So, we can now calculate the ratio.
\[Ratio = \dfrac{{60units}}{{120units}}\]
Cutting zeros from numerator and denominator.
\[Ratio = \dfrac{6}{{12}}\]
Now let’s divide with 6 from numerator and denominator.
\[Ratio = \dfrac{1}{2}\]
Now, 1 is not divisible by 2. Means we have got our ratio that is \[1:2\].
\[Ratio = 1:2\]

Note: We can calculate the ratio of both values once both values are in the same quantity if it’s not then convert them all into the smallest unit but check that both should be in the same units. Then divide the appropriate number from the numerator and the denominator until the numerator is not divisible by the denominator.