Question

In a playground, kids are playing in the groups of $5$ . If there is one group of kids, then, \[total\text{ }number\text{ }of\text{ }kids\text{ }=\text{ }5\] If there is two group of kids, then, \[total\text{ }number\text{ }of\text{ }kids\text{ }=\text{ }5+5=5\times 2\] and so on. So the total number of kids playing in the playground are \[5+5+5+....=5\times n\] Here, the variable n is?

Answer 1

Hint: For solving these types of questions, we need to have a clear understanding about the number of items and how groups are formed. By carefully going through the question, we can easily understand what the variable n stands for.

Complete step by step answer:
The multiples of an entire number are found by taking the product for any counting number which integers. For example, to seek out the multiples of three, multiply $3$ by $1$ , $3$ by $2$ , $3$ by $3$ , and so on. For finding the multiples of $5$ , we multiply $5$ by 1,5 by $2$ , $5$ by $3$ , and so on and on. The multiples are the products of these multiplications. Some examples of multiples can be found below. In every given example, the counting numbers $1$ through $8$ is used. However, the list of multiples for an entire number is endless. These values are called multiples as these values are obtained by adding or subtracting the original value repeatedly. A common multiple can be defined as a number that is a multiple of two or more numbers in a given set. We know that both multiplication and division are the inverse operations. It implies both are linked with each other. can find out using division whether a given number is multiple of another number or not.
In the given problem, $5$ kids are supposed to be one and 5+5 signifies $2$ groups, or we can say that it is also represented by $5\times 2$ . Similarly, $3$ groups would be $5+5+5$ or $5\times 3$ . Hence here $1,2,3$ all represent the number of groups of kids. Or we can also say that n number of groups would signify \[5+5+5+5+....n\] number of times or $5\times n$ .
Hence, the variable n signifies the number of groups of kids.

Note: These types of problems are pretty easy to solve, but the most common mistakes that students tend to make is that they might confuse the variable n as the number of kids instead of the number of groups of kids. One needs to be careful otherwise small misjudgements can lead to a totally different answer.