Question

Express the ratio expression in simplest form: 40 Kg: 1 quintal.

Answer 1

Hint: When we find the ratio between two different units then convert the bigger unit into smaller units. Ratio of any expression is only carried when units are the same. After converting the units simplify the expression unit it becomes indivisible.

Complete step-by-step answer:
The given expression for the simplification is: 40 Kg: 1 quintal.
First writing the given expression in $ \dfrac{p}{q} $ form then we get,
 $ \Rightarrow \dfrac{{40\;{\rm{kg}}}}{{1\;{\rm{quintal}}}} $
Now we will convert the quintal quantity in kilogram. As quintal is a bigger unit and kilogram is a smaller unit.
As we know that, there are 100 kg in one quintal so,
 $ \Rightarrow {\rm{1}}\;{\rm{quintal = 100}}\;{\rm{kg}} $
Writing the value of 1 quintal which in form of kg then we get,
 $ \Rightarrow \dfrac{{40\;{\rm{kg}}}}{{100\;{\rm{kg}}}} $
Now, we can easily cancel out the same units in the expression then we get,
 $ \Rightarrow \dfrac{{40\;}}{{100}} $
Here, we will get the fraction form so, solving this fraction form till it didn’t become indivisible then we get,
 $ \dfrac{2}{5} $
Here 2 and 5 are never divided by the same number hence it is the simplest form.
Hence the simplest form of the given expression 40 Kg: 1 quintal is $ \dfrac{2}{5} $ .

Note: In this type of question, convert the bigger unit into smaller units. When we convert the bigger unit into a smaller unit then the number of smaller units present in one bigger unit is multiplied with the bigger unit and when we convert the smaller unit into a bigger unit then the number of smaller units present in one bigger unit divides the smaller unit. To get the ratio of any expression it is compulsory to make the units similar.