Question

How do you divide: \[\left( -120 \right)\div \left( +10 \right)\]?

Answer 1

Hint: Write the given number (-120) as (-1) \[\times \] 120. Now, to divide 120 with 10, take the reciprocal of 10 and multiply it with 120. Cancel the common factors to simplify the product. Now, multiply (-1) with the obtained product to get the answer.

Complete step by step answer:
Here, we are asked to divide (-120) by (+10). So, the dividend is -120 and the divisor is +10.
Now, when we have to divide a number ‘a’ with another number ‘b’ then what we do is, we first take the reciprocal of the number ‘b’ and then multiply it with number ‘a’. To take the reciprocal of a number we divide 1 by that number. For example: - reciprocal of b will be \[\dfrac{1}{b}\].
So, let us come to the question. Taking the reciprocal of 10 we get, \[\dfrac{1}{10}\]. Now, we have to multiply \[\dfrac{1}{10}\] with (-120).
So, we get,
\[\Rightarrow \left( -120 \right)\div 10=\left( -120 \right)\times \dfrac{1}{10}\]
The above expression can also be written as: -
\[\Rightarrow \left( -120 \right)\div 10=\left( -1 \right)\times 120\times \dfrac{1}{10}\]
Therefore, we need to multiply 120 and \[\dfrac{1}{10}\] first, so we get,
\[\Rightarrow \left( -120 \right)\div 10=\left( -1 \right)\times \dfrac{120}{10}\]
Cancelling the common factor, i.e., 10, we get,
\[\Rightarrow \left( -120 \right)\div 10=\left( -1 \right)\times 12\]
Now, multiplying (-1) with the obtained product 12, we get,
\[\Rightarrow \left( -120 \right)\div 10=-12\]

Hence, -12 is the required answer.

Note: One may note that we are getting a negative answer. This is because only one of the two provided numbers were negative. If both the numbers would have been negative then we would have obtained a positive answer by using the property: - \[\left( -1 \right)\times \left( -1 \right)=1\]. Remember that here we are not actually dividing -120 with 10, we are dividing 120 with 10 and taking its product with -1. You must know the definition of reciprocal and how to calculate the reciprocal of a number.