Answer :
To solve this problem and find which expressions have negative quotients, let's analyze each expression individually. Remember that a quotient (result of division) is negative if one number is positive and the other is negative.
1. Expression: [tex]$1.4 \div 99.9$[/tex]
- Here, both numbers (1.4 and 99.9) are positive.
- A positive number divided by another positive number will always result in a positive quotient.
- Therefore, this expression does not have a negative quotient.
2. Expression: [tex]$5.7 \div -2.2$[/tex]
- The numerator (5.7) is positive, and the denominator (-2.2) is negative.
- Dividing a positive number by a negative number will result in a negative quotient.
- Therefore, this expression has a negative quotient.
3. Expression: [tex]$-0.01 \div 0.05$[/tex]
- The numerator (-0.01) is negative, and the denominator (0.05) is positive.
- Dividing a negative number by a positive number will result in a negative quotient.
- Therefore, this expression has a negative quotient.
4. Expression: [tex]$-3 \div -0.009$[/tex]
- Both the numerator (-3) and the denominator (-0.009) are negative.
- Dividing a negative number by another negative number will result in a positive quotient.
- Therefore, this expression does not have a negative quotient.
5. Expression: [tex]$0 \div -8.6$[/tex]
- Here, the numerator is 0, and the denominator is negative (-8.6).
- Dividing zero by any non-zero number results in zero, which is neither positive nor negative.
- Therefore, this expression does not have a negative quotient.
Based on the analysis, the expressions that result in negative quotients are:
- [tex]$5.7 \div -2.2$[/tex]
- [tex]$-0.01 \div 0.05$[/tex]
These are the expressions with negative quotients.
1. Expression: [tex]$1.4 \div 99.9$[/tex]
- Here, both numbers (1.4 and 99.9) are positive.
- A positive number divided by another positive number will always result in a positive quotient.
- Therefore, this expression does not have a negative quotient.
2. Expression: [tex]$5.7 \div -2.2$[/tex]
- The numerator (5.7) is positive, and the denominator (-2.2) is negative.
- Dividing a positive number by a negative number will result in a negative quotient.
- Therefore, this expression has a negative quotient.
3. Expression: [tex]$-0.01 \div 0.05$[/tex]
- The numerator (-0.01) is negative, and the denominator (0.05) is positive.
- Dividing a negative number by a positive number will result in a negative quotient.
- Therefore, this expression has a negative quotient.
4. Expression: [tex]$-3 \div -0.009$[/tex]
- Both the numerator (-3) and the denominator (-0.009) are negative.
- Dividing a negative number by another negative number will result in a positive quotient.
- Therefore, this expression does not have a negative quotient.
5. Expression: [tex]$0 \div -8.6$[/tex]
- Here, the numerator is 0, and the denominator is negative (-8.6).
- Dividing zero by any non-zero number results in zero, which is neither positive nor negative.
- Therefore, this expression does not have a negative quotient.
Based on the analysis, the expressions that result in negative quotients are:
- [tex]$5.7 \div -2.2$[/tex]
- [tex]$-0.01 \div 0.05$[/tex]
These are the expressions with negative quotients.
