Question

Express the following percentage as ratio in the reduced form.
52 : 100

Answer 1

Hint: Given percentage (as ratio) is 52 : 100
Next, break 52 and 100 in factors to find their HCF.
 Now, we can write 52 : 100 as $\dfrac{{52}}{{100}}$ and divide both numerator and denominator with the HCF to find the reduced form.

Complete step-by-step answer:
Given percentage is 52 : 100 (i.e. 52%)
Now,
52 = 2 × 2 × 13
100 = 2 × 2 × 5 × 5
Therefore, one may see that HCF of 52 and 100 is 4
Now, required ratio is
$ = \dfrac{{52}}{{100}}$
On dividing the numerator and denominator by 4, we get
 $ = \dfrac{{\left( {\dfrac{{52}}{4}} \right)}}{{\left( {\dfrac{{100}}{4}} \right)}}$
On simplification we get,
$ = \dfrac{{13}}{{25}}$
$ = 13\,\,:\,\,25$
Hence expressing the given percentage as a ratio in the reduced form, we get $13\,\,:\,\,25$.

Note: Ratio: The comparison or simplified form of two quantities of the same kind is referred to as ratio. This relation gives us how many times one quantity is equal to the other quantity. In other words, the ratio is the number which can be used to express one quantity as a fraction of the other ones.
The two numbers in a ratio can only be compared when they have the same unit.
 Percentage: Percentage literally means ‘per hundred’. In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
 When a percentage x% is given and we have to express it as a ratio in the reduced form, we have to break x and 100 in factors to find their HCF.
 Now, we can write x : 100 as $\dfrac{x}{{100}}$ and divide both numerator and denominator with the HCF to find the reduced form.