Question

What is 10 divided by -4?

Answer 1

Hint: Assume the given expression as E. Write the given negative number (-4) as (-1) \[\times \] 4. Now, to divide 10 by 4, take the reciprocal of 4 and multiply it with 10. 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 solution:
Here we have been asked to divide 10 by -4. So the dividend is 10 and the divisor is -4. Let us assume this expression as E, so we have,
$\Rightarrow E=10\div \left( -4 \right)$
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 -4 we get \[\dfrac{1}{\left( -4 \right)}\] which can be written as \[\left( -\dfrac{1}{4} \right)\]. Now, we have to multiply \[\left( -\dfrac{1}{4} \right)\] with 10. So we get,
\[\Rightarrow E=\left( 10 \right)\times \left( -\dfrac{1}{4} \right)\]
The above expression can also be written as: -
\[\Rightarrow E=\left( -1 \right)\times 10\times \dfrac{1}{4}\]
Therefore we need to multiply 10 and \[\dfrac{1}{4}\] first, so we get,
\[\Rightarrow E=\left( -1 \right)\times \dfrac{10}{4}\]
Let us write the numerator and the denominator as the product of their primes so that we may cancel the common factors and simplify.
\[\Rightarrow E=\left( -1 \right)\times \dfrac{2\times 5}{2\times 2}\]
Cancelling the common factors we get,
\[\begin{align}
  & \Rightarrow E=\left( -1 \right)\times \dfrac{5}{2} \\
 & \therefore E=-\dfrac{5}{2} \\
\end{align}\]
Hence $\left( \dfrac{-5}{2} \right)$ is the answer.

Note: Remember that $\left( -1 \right)\times 1=-1$ and $\left( -1 \right)\times \left( -1 \right)=1$. This is the basic rule to determine if the number obtained by the mathematical operation will be positive or negative. Note that we are not actually dividing -10 by 4, we are dividing 10 by 4 and taking its product with -1, because we don’t divide a negative number by a positive or a positive number by a negative number. If we will do so it will violate the division algorithm as the quotient will become negative.