Question

How do you find the quotient of $-\dfrac{150}{10}$? \[\]

Answer 1

Hint: We recall dividend, divisor, quotient and remainder from division operation. Since in the given division numerator which is dividend is negative and denominator is positive then quotient will be negative. So we forget the negative sign and divide to get the quotient. We put negative signs on it. \[\]

Complete step by step answer:
We know that in arithmetic operation of division the number we are going to divide is called dividend, the number by which divides the dividend is called divisor. We get a quotient which is the number of times the divisor is of dividend and in the end remainder . If the number is $n$, the divisor is $d$, the quotient is $q$ and the remainder is $r$, they are related by the following equation,
\[n=dq+r\]
Here the divisor can never be zero. The above relation is called Euclid’s division Lemma. If we take $q$ as decimal or fractional we shall always get $r=0$ and
\[n=dq+r=dq\]
When we are given a number rational from $\dfrac{a}{b}$ we take the numerator as the dividend and denominator as the divisor. We are asked in the question to find the quotient of $-\dfrac{150}{10}=\dfrac{-150}{10}$. So here the dividend is the numerator $-150$ and the divisor is the denominator 10. We know that the product of two numbers is negative when exactly one of the numbers is negative. Since here the divisor 10 here is positive the quotient will be negative. We first forget the negative sign on the dividend 150 and divide 10 to have;
\[150\div 10=15\]
So the quotient by putting negative sign is $-15$. \[\]

Note:
We can alternatively use factorization to find the quieting quotient as
\[\dfrac{-150}{10}=\dfrac{-15\times 10}{1\times 10}=-\dfrac{15}{1}\times \dfrac{10}{10}\]
Since a number divided by itself is 1 we use have $\dfrac{10}{10}=1$ and get
\[\dfrac{-150}{10}=\dfrac{-15\times 10}{1\times 10}=-\dfrac{15}{1}\times \dfrac{10}{10}=\dfrac{-15}{1}\times 1\]
Since a number multiplied or divided by 1 in the same number we have
\[\dfrac{-150}{10}=\dfrac{-15\times 10}{1\times 10}=-\dfrac{15}{1}\times \dfrac{10}{10}=\dfrac{-15}{1}\times 1=\dfrac{-15}{1}=-15\]
So the quotient is 15.