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Answer :
To find out which expressions result in negative quotients, let's consider each expression with signed decimal numbers individually:
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- A positive number divided by a positive number results in a positive quotient.
- Therefore, the quotient is not negative.
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive, and the second number is negative.
- A positive number divided by a negative number results in a negative quotient.
- Therefore, the quotient is negative.
3. Expression: [tex]\(-0.01 \div 0.05\)[/tex]
- The first number is negative, and the second number is positive.
- A negative number divided by a positive number results in a negative quotient.
- Therefore, the quotient is negative.
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- A negative number divided by a negative number results in a positive quotient.
- Therefore, the quotient is not negative.
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- The numerator (0) divided by any non-zero number results in zero.
- Zero is neither positive nor negative.
- Therefore, the quotient is not negative.
Based on the analysis above, the expressions that have negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
So, the expressions with negative quotients are the second and third ones.
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- A positive number divided by a positive number results in a positive quotient.
- Therefore, the quotient is not negative.
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive, and the second number is negative.
- A positive number divided by a negative number results in a negative quotient.
- Therefore, the quotient is negative.
3. Expression: [tex]\(-0.01 \div 0.05\)[/tex]
- The first number is negative, and the second number is positive.
- A negative number divided by a positive number results in a negative quotient.
- Therefore, the quotient is negative.
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- A negative number divided by a negative number results in a positive quotient.
- Therefore, the quotient is not negative.
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- The numerator (0) divided by any non-zero number results in zero.
- Zero is neither positive nor negative.
- Therefore, the quotient is not negative.
Based on the analysis above, the expressions that have negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
So, the expressions with negative quotients are the second and third ones.
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