Question

If the dividend and the divisor have like signs then the quotient will be ________.
(a) Positive
(b) Negative
(c) Zero
(d) None of these

Answer 1

Hint: We have to check what will be the sign of the quotient when the dividend and the divisor have like a sign. Like sign means having the same sign, it can be both positive or both negative. Then we will check how the sign of the quotient came on treating different signs of the dividend and the divisor together.

Complete step-by-step answer:
Let us consider the following cases with different signs of dividend and the divisor.
Case 1: When both the dividend and the divisor are positive.
Dividend = 160
Divisor = 20
So,
\[\text{Quotient}=\dfrac{\text{Dividend}}{\text{Divisor}}=\dfrac{160}{20}=8\left( \text{positive} \right)\]
So, when both are positive, we get quotient as positive.
Case 2: When both are negative.
Dividend = – 40
Divisor = – 10
So,
\[\text{Quotient}=\dfrac{\text{Dividend}}{\text{Divisor}}=\dfrac{-40}{-10}=\dfrac{40}{10}=4\left( \text{positive} \right)\]
When both are negative, then again the quotient is positive.
Case 3: The dividend is negative and the divisor is positive.
Divisor = 2
Dividend = – 8
So,
\[\text{Quotient}=\dfrac{\text{Dividend}}{\text{Divisor}}=\dfrac{-8}{2}=-4\left( \text{negative} \right)\]
When the dividend is negative and the divisor is positive, the quotient is negative.
Case 4: The dividend is positive and the divisor is negative.
Dividend = 20
Divisor = – 4
So,
\[\text{Quotient}=\dfrac{\text{Dividend}}{\text{Divisor}}=\dfrac{20}{-4}=-5\left( \text{negative} \right)\]
When the dividend is positive and the divisor is negative, the quotient is negative.
So, we get when both the divisor and the dividend are of the same sign (alike) then the quotient comes out as positive.
Hence, option (a) is the right answer.

Note: Do not get confused over the divisor and the dividend. Remember that when negative is divided by negative, always produce a positive. Take a simple example as we have to focus more on signs and not on digits. So, simple terms will make it work easily.