Question

Ravi had $\dfrac{5}{6}$ of a cake. He ate $\dfrac{2}{3}$ of it. What part of the cake did he eat?
A. $\dfrac{5}{9}$
B. $\dfrac{10}{12}$
C. $\dfrac{10}{6}$
D. $\dfrac{10}{3}$

Answer 1

Hint: In the given question, we are supposed to find the part of the cake Ravi ate. We solve the given question by multiplying the fraction $\dfrac{5}{6}$ and a fraction $\dfrac{2}{3}$ . The product between the two will give us the required result.

Complete step by step answer:
Ravi had $\dfrac{5}{6}$ of a cake and he ate $\dfrac{2}{3}$ of it. We are asked to find the part of the cake that ravi had. We will be solving the given question by finding out the product between the two given fractions.
A fraction, in mathematics, represents a part of a whole thing. It consists of two parts namely,
numerator, denominator.
The number on the top is called the numerator.
The number on the bottom is called the denominator.
Let us understand the concept of the fraction with an example as follows,
Example:
$\Rightarrow \dfrac{a}{b}$
In the above fraction,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
According to the question,
Ravi had $\dfrac{5}{6}$ of a cake and he ate $\dfrac{2}{3}$ of it.
We will be finding the part of the cake Ravi had by multiplying the fractions $\dfrac{5}{6}$ and $\dfrac{2}{3}$
$\Rightarrow \dfrac{5}{6}\times \dfrac{2}{3}$
According to the rules of fractions,
The multiplication of fractions is done by multiplying the numerators and denominators of the fraction, respectively.
Applying the same, we get,
$\Rightarrow \dfrac{5\times 2}{6\times 3}$
Simplifying the above fraction, we get,
$\Rightarrow \dfrac{10}{18}$
Cancelling out the common factors, we get,
$\Rightarrow \dfrac{5}{9}$

So, the correct answer is “Option A”.

Note: The result obtained in the given question can be cross-checked as follows,
The division of the result obtained and $\dfrac{2}{3}$ must result in $\dfrac{5}{6}$
From the above, the result obtained is $\dfrac{5}{9}$
Substituting the same, we get,
$\Rightarrow \dfrac{\left( \dfrac{5}{9} \right)}{\left( \dfrac{2}{3} \right)}$
The above expression can be written as follows,
$\Rightarrow \dfrac{5\times 3}{9\times 2}$
Canceling the common factors, we get,
$\Rightarrow \dfrac{5}{3\times 2}$
Simplifying the above expression, we get,
$\Rightarrow \dfrac{5}{6}$
The result obtained is correct.