Question

Neha was given $\dfrac{5}{7}$ of a basket of bananas. What fraction of bananas was left in the basket?

Answer 1

Hint: Assume the total number of bananas in the basket as x. Now, find the number of bananas that Neha is provided with by taking the product of $\dfrac{5}{7}$ with x. To find the number of bananas she was left with, subtract the above obtained product from x. Finally, divide the obtained difference by x to get the answer.

Complete step by step solution:
Here we have been provided with the information regarding the fraction of bananas that Neha is provided from a basket. We have been asked to find the fraction of bananas left in the basket.
Let us assume the total number of bananas in the basket was x. So the total number of bananas she is given will be equal to the product of the fraction of bananas given to her and x. Therefore we get,
$\Rightarrow $ Number of bananas given to Neha = $\dfrac{5x}{7}$
$\Rightarrow $ Number of bananas left in the basket = $x-\dfrac{5x}{7}$
Taking L.C.M and simplifying we get,
$\Rightarrow $ Number of bananas left in the basket = \[\dfrac{7x-5x}{7}\]
$\Rightarrow $ Number of bananas left in the basket = \[\dfrac{2x}{7}\]
Therefore the fraction of bananas left in the basket will be equal to the ratio of number of bananas left and x, so we get,
$\Rightarrow $ Fraction of bananas left in the basket = \[\dfrac{2x}{7x}\]
$\therefore $ Fraction of bananas left in the basket = \[\dfrac{2}{7}\]
Hence, the fraction of bananas left in the basket is $\dfrac{2}{7}$.

Note: Note that you can directly get the answer by subtraction the given fraction $\dfrac{5}{7}$ from 1, however this direct approach is derived using the above process we have followed to get the answer. Here x can be any positive integer value. It cannot be any negative integer, 0 or any fractional value because the total number of bananas will always be counted as a whole unless some special condition is provided in the question regarding its fractional value like half, one – fourth etc.