Question

How do you evaluate $91 \times \dfrac{3}{{13}}$?

Answer 1

Hint: We are given an expression which is a product of a whole number and a fraction. In questions like this, we try to simplify the expression by cancelling out the common factor between the numerator and the denominator. The easiest way to do so is to write all the numbers as the product of their prime factors and then cancel out the common factors. The left factors can be then multiplied and written as the final answer.

Complete step by step solution:
(i) We are given
$91 \times \dfrac{3}{{13}}$
Here, we know that $91$ is a whole number. Therefore, we can also write it as:
$\dfrac{{91}}{1} \times \dfrac{3}{{13}}$
Now that we can clearly see which number is a numerator and which is a denominator, we will write every number as the product of its prime factors.
Since we know that $3$ and $13$ are already prime numbers, we will only expand $91$ as the product of its prime factors. So,
$91 = 7 \times 13$
Therefore, our expression becomes:
$\dfrac{{7 \times 13}}{1} \times \dfrac{3}{{13}}$
(ii) Now, our next step would be to cancel out the common factors between the numerator and the denominator.
As we can see, we have $13$ in the numerator as well as in the denominator. Therefore, we can directly cancel it out from the numerator and the denominator.
Therefore, now our expression will become:
$\dfrac{7}{1} \times \dfrac{3}{1}$
(iii) Now, we can see that there are no common factors left between the numerator and the denominator so will simply multiply the numerator with numerator and denominator with denominator i.e., we will multiply $7$ with $3$ in the numerator and $1$ with $1$ in the denominator.
Therefore, we will get
$\dfrac{{21}}{1}$
Which can be simply written as $21$.
Hence, $91 \times \dfrac{3}{{13}} = 21$

Note: After some practice we can directly see the common factors between two numbers without expanding them as the product of their prime factors. In that case, we can directly cancel them out i.e., when we saw $91$ in the numerator and $13$ in the denominator, we could have directly written $7$ in the numerator because we know that $13 \times 7 = 91$. Another case can be when there is no common factor or we are facing difficulty to find the common factor. In that case we can simply multiply numerator with numerator and denominator with denominator and then solve the obtained fraction by long division method.