Question

What should be multiplied by $-23$ to get 575?
(a) 15
(b) 25
(c) $-25$
(d) 35

Answer 1

Hint: We have to find a number $n$ such that when we multiply $n$ and $-23$, we get 575. We will figure out the sign of the number $n$ using the given numbers. Then we will see the relation between multiplication and division. We will divide the number 575 by 23 to find the number $n$ and then associate its sign to it.

Complete step by step answer:
Let the number that needs to be multiplied by $-23$ to get 575 be $n$. We know that we get a positive number if we multiply two positive numbers or if we multiply two negative numbers. We get a negative number if we multiply one negative number with one positive number. We are aware that $-23$ is a negative number and 575 is a positive number. Therefore, we should multiply a negative number to $-23$ to get 575. Hence, the number $n$ is a negative number.
Now, we will look at the relation between multiplication and division. Let us multiply two numbers, $a$ and $b$, to get the number $c$. So, we have $a\times b=c$. We can write $a=\dfrac{c}{b}$, which means we divide $c$ by $b$ to obtain the value of $a$. We will use this relation between multiplication and division to find the number $n$.
Let us divide 575 by 23. We get the following,
$\dfrac{575}{23}=25$
We already know that the number $n$ is negative. Hence, we will multiply $-23$ by the number $-25$ to obtain 575.

So, the correct answer is “Option c”.

Note: It is essential that we understand the concept of multiplication and division. We should be familiar with the way the signs of numbers are affected while performing multiplication or division. Since 23 is a prime number, it is useful to be familiar with its multiplication table so that we can do the calculation quickly. Alternatively, we can factorize the number 575 into its prime factors and find the number $n$ and then associate the negative sign to it.