Question

How many $\dfrac{5}{6}$’s are in $1$?

Answer 1

Hint:In this question we need to find there are how many $\dfrac{5}{6}$’s will sum up to $1$. In this question we have to find how many times do we add $\dfrac{5}{6}$ to get $1$ or do we need to find with which number we multiply $\dfrac{5}{6}$ so that we get $1$. This question is similar to finding the multiplicative inverse of a number. This question is a very basic one to try once before looking at a complete solution.

Complete step by step solution:
Let us try to solve this question in which we are asked to find the number of $\dfrac{5}{6}$, so that they add up to $1$. To solve this question we are required to have knowledge of addition and multiplication of numbers. To solve this also we need to know the relation between addition and multiplication. Addition of a number $n$ times is equal to multiplying a number by $n$, in mathematical equation
$
a + a + a + ... + a = \,n \cdot a \\
\,\,\,\,\,\,\,'n\,times'\,\,a \\
$
For example, if we have to add $5$ times $2$ it is the same as multiplying $5$ with $2$.
$
2 + 2 + 2 + 2 + 2 = 5 \cdot 2 \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10 = 10 \\
$
In our question we have to find how many $\dfrac{5}{6}$ add up to become equal to $1$.
Let’s suppose that adding ‘$n$’ times $\dfrac{5}{6}$ we get $1$. In mathematical equation
$
\dfrac{5}{6} + \dfrac{5}{6} + \dfrac{5}{6} + ... + \dfrac{5}{6} = 1 \\
\,\,\,\,\,\,\,\,\,\,n\,times \\
$ $eq(1)$
Now using the relation between addition and multiplication of a number we can write $eq(1)$.
As follows,
$\dfrac{5}{6} \cdot n = 1$ $eq(2)$
Now multiplying with $6$and dividing with$5$$eq(2)$, we get the value of $n$equal to
$n = \dfrac{6}{5}$
Hence there are $\dfrac{6}{5}$,$\dfrac{5}{6}$'s in $1$.

Note: While solving these types of questions we just need to know that addition of a number $n$ times is the same as multiplying that number by $n$. The number of $\dfrac{6}{5}$ is called the multiplicative inverse of $\dfrac{5}{6}$. Multiplicative inverse of a number is the number with which we multiply the number to get $1$ in answer.