Question

How do you simplify the fraction $\dfrac{{25}}{{45}}$?

Answer 1

Hint: We will first write the prime factorisation of both the numbers involved in the numerator and denominator. Then, we can cross off the similar terms and thus have the fraction in lowest terms.

Complete step by step answer:
We are given that we are required to simplify the fraction $\dfrac{{25}}{{45}}$.
Since, we see that its numerator is 25 and the denominator is 45.
We also know that 25 is the square of 5, therefore can be written as follows:-
$ \Rightarrow 25 = 5 \times 5$
We also know that 45 is the multiple of 5, 3 and 3, therefore can be written as follows:-
$ \Rightarrow 45 = 3 \times 3 \times 5$
Therefore, the fraction can now be written as follows:-
\[ \Rightarrow \dfrac{{25}}{{45}} = \dfrac{{5 \times 5}}{{3 \times 3 \times 5}}\]
Since, there is a 5 common in both the numerator and denominator on the right hand side of the above mentioned expression, we can cancel it out to obtain the following:-
\[ \Rightarrow \dfrac{{25}}{{45}} = \dfrac{5}{{3 \times 3}}\]
Now, simplifying the denominator of the right hand side of the above mentioned expression, we will then obtain the following expression with us:-
\[ \Rightarrow \dfrac{{25}}{{45}} = \dfrac{5}{9}\]
Hence, we have the required answer.

Note: The students must note that we could cancel off the 5 from both the numerator and the denominator because we know that 5 can never be equal to zero. If we have any common variable in numerator and denominator, then we can never cancel it unless we are sure that it can never be equal to 0. If it even has the slightest possibility of being equal to zero, we can never cancel it off.
The students must also note that we broke it off in prime factorisation so that we can find out the common factors from both the numbers. If we would have written 45 as multiple of 15 and 3, then we would not have been able to find the common 5 in 25 and 45. Therefore, always break the numbers into its prime factorisation.