Question

What is -72 divided by 8?

Answer 1

Hint: Assume the given expression as E. Write the given negative number (-72) as (-1) \[\times \] 72. Now, to divide 72 with 8, take the reciprocal of 8 and multiply it with 72. Cancel the common factors by writing the numbers as the product of their prime factors to simplify the product. Now, multiply (-1) with the obtained product to get the answer.

Complete step by step answer:
Here we have been asked to divide -72 by 8. So the dividend is -72 and the divisor is 8. Let us assume this expression as E, so we have,
$\Rightarrow E=-72\div 8$
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 8 we get \[\dfrac{1}{8}\]. Now, we have to multiply \[\dfrac{1}{8}\] with $-72$, So we get,
\[\Rightarrow E=\left( -72 \right)\times \dfrac{1}{8}\]
The above expression can also be written as: -
\[\Rightarrow E=\left( -1 \right)\times 72\times \dfrac{1}{8}\]
Therefore we need to multiply 120 and \[\dfrac{1}{8}\] first, so we get,
\[\Rightarrow E=\left( -1 \right)\times \dfrac{72}{8}\]
Let us write the numerator and the denominator as the product of their primes so that we may cancel the common factors and simplify.
\[\Rightarrow E=\left( -1 \right)\times \dfrac{2\times 2\times 2\times 3\times 3}{2\times 2\times 2}\]
Cancelling the common factors we get,
\[\begin{align}
  & \Rightarrow E=\left( -1 \right)\times \dfrac{3\times 3}{1} \\
 & \Rightarrow E=\left( -1 \right)\times 9 \\
 & \therefore E=-9 \\
\end{align}\]

Hence -9 is the 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 -72 by 8, we are dividing 72 by 8 and taking its product with -1. You must know how to find the reciprocal of a number.