Question

How do find $35$ divided by $\left( { - 70} \right)$ ?

Answer 1

Hint: Here we use the rule for dividing positive and negative rational numbers. To solve this given numbers. On doing some simplification we get the required answer.

Complete step-by-step solution:
If the numbers have the same sign (both positive and both negative), then the answer is positive. If the numbers have opposite signs (one is positive and the other is negative), then the answer is negative.
One way of explaining this, the rule for dividing is the same rule for multiplying positive and negative numbers. The rule is the same because division is multiplying by the reciprocal. The reciprocal of a positive number is positive and the reciprocal of a negative number is negative.
The reciprocal of $\dfrac{p}{q}$ is $\dfrac{1}{{\dfrac{p}{q}}}$ which is the same as $\dfrac{q}{p}$ .
The reciprocal of a number is the number we have to multiply by to get $1$ . Not every number has a reciprocal. $0$ does not have a reciprocal (because $0$ times any number is $0$).
Here we are going to divide the number $35$ into $\left( { - 70} \right)$ that is,
$ \Rightarrow \dfrac{{35}}{{ - 70}}$
Now find the greatest common factor of both numbers $35$ and $\left( { - 70} \right)$ we get $35$ ,
So we divide this number into the numerator and also the denominator we get,
$ \Rightarrow \dfrac{{35 \div 35}}{{ - 70 \div 35}}$
Now simplifying the above term we get,
$ \Rightarrow \dfrac{1}{{ - 2}}$
The simplification of the term $35$ divided by $\left( { - 70} \right)$ is $\dfrac{1}{{ - 2}}$ .

The decimal value of the answer is $ - 0.5$.

Note: We can also solve this problem using long division method before you continue, note that in the problem $35$ divided by $\left( { - 70} \right)$the numbers are defined as follows:
$35 = $ Dividend
$ - 70 = $ Divisor
$\begin{array}{*{20}{c}}
  {\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,0.5} \\
  {70)\overline {35} } \\
  {\,\,\,\,\,\,\,\,\underline {35} }
\end{array}} \\
  {\,\,\,\,\,\,\,\,\,0}
\end{array}$
Here we divide $70$ as divisor, but our divisor is $ - 70$ so we get the quotient is $ - 0.5$