check whether (-75) divide 5 and 75 divide (-5) are equal
The Correct Answer and Explanation is:
To check if the two expressions, (−75)÷5(-75) \div 5(−75)÷5 and 75÷(−5)75 \div (-5)75÷(−5), are equal, let’s first evaluate both individually.
First Expression: (−75)÷5(-75) \div 5(−75)÷5
Dividing −75-75−75 by 555 gives:(−75)÷5=−15(-75) \div 5 = -15(−75)÷5=−15
The result is −15-15−15, since dividing a negative number by a positive number results in a negative quotient.
Second Expression: 75÷(−5)75 \div (-5)75÷(−5)
Now, dividing 757575 by −5-5−5 gives:75÷(−5)=−1575 \div (-5) = -1575÷(−5)=−15
Here, dividing a positive number by a negative number also results in a negative quotient. The result is −15-15−15.
Conclusion
Both expressions (−75)÷5(-75) \div 5(−75)÷5 and 75÷(−5)75 \div (-5)75÷(−5) yield the same result of −15-15−15. Therefore, the two expressions are indeed equal.
The general rule for division is that if you divide a positive number by a negative number, or a negative number by a positive number, the quotient will always be negative. The magnitude of the quotient is unaffected by whether the negative sign appears in the numerator or the denominator; only the sign changes.
