Question

Find the equivalent fraction of $\dfrac{15}{35}$ with denominator 7.

Answer 1

Hint: We will use the concept of multiples in which we will write the given numbers in terms of their multiples and cancel the common terms to get the required solution. This method is an easy method to get the fraction into its simpler terms.

Complete step-by-step answer:
We will first consider the fraction that is given to us as $\dfrac{15}{35}$. Now, we will find the multiples of these two numbers which are 15 and 35. The numbers that divide 15 are 1, 3, 5 and 15. These numbers are also known as the factors of 15. Now, we will consider the number 15 as a product of 1, 3 and 5. Now, we will collect the numbers which divide 35. These numbers are 1, 5, 7 and 35. These numbers are also the factor of 35. Now we will write 35 as a product of 1, 5 and 7.
Now, we will substitute in the fraction like so $\dfrac{15}{35}=\dfrac{1\times 3\times 5}{1\times 5\times 7}$. After this we will cancel the common terms in the numerator and denominator of the fraction. The numbers that are going to be cancelled are 1 and 5. Thus, we will get $\dfrac{15}{35}=\dfrac{3}{7}$. As we can clearly see that the number 7 is in the denominator of the fraction so, this is going to be the required equivalent fraction of $\dfrac{15}{35}$. Hence, the equivalent fraction of $\dfrac{15}{35}$ is $\dfrac{3}{7}$.

Note: We can also solve it directly. This can be done as by finding the common numbers between the numerator and denominator of the given fraction. As we can clearly see that the numbers 15 and 35 both are the multiples of 5 so, we can divide these two numbers by 5. Also, we can divide both numerator and denominator by 5 and then get the right answer. We need to take care while multiplying the terms as well as if using the alternate method then we need to divide in a correct way otherwise the answer will be wrong.