Answer :
To determine which expressions have negative quotients, we need to understand the rules for dividing signed numbers:
1. Positive ÷ Positive results in a positive quotient.
2. Positive ÷ Negative or Negative ÷ Positive results in a negative quotient.
3. Negative ÷ Negative results in a positive quotient.
4. Zero ÷ any nonzero number results in zero (but since it is neither negative nor positive, we do not consider it negative).
Now let's evaluate each expression step-by-step to determine which ones have negative quotients:
- [tex]$1.4 \div 99.9$[/tex]:
- Both numbers are positive.
- According to rule 1, the quotient is positive.
- [tex]$5.7 \div -2.2$[/tex]:
- One number is positive, and the other is negative.
- According to rule 2, the quotient is negative.
- [tex]$-0.01 \div 0.05$[/tex]:
- One number is negative, and the other is positive.
- According to rule 2, the quotient is negative.
- [tex]$-3 \div -0.009$[/tex]:
- Both numbers are negative.
- According to rule 3, the quotient is positive.
- [tex]$0 \div -8.6$[/tex]:
- Zero divided by a negative number.
- According to rule 4, the quotient is zero, which is not considered negative.
Based on this 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. Positive ÷ Positive results in a positive quotient.
2. Positive ÷ Negative or Negative ÷ Positive results in a negative quotient.
3. Negative ÷ Negative results in a positive quotient.
4. Zero ÷ any nonzero number results in zero (but since it is neither negative nor positive, we do not consider it negative).
Now let's evaluate each expression step-by-step to determine which ones have negative quotients:
- [tex]$1.4 \div 99.9$[/tex]:
- Both numbers are positive.
- According to rule 1, the quotient is positive.
- [tex]$5.7 \div -2.2$[/tex]:
- One number is positive, and the other is negative.
- According to rule 2, the quotient is negative.
- [tex]$-0.01 \div 0.05$[/tex]:
- One number is negative, and the other is positive.
- According to rule 2, the quotient is negative.
- [tex]$-3 \div -0.009$[/tex]:
- Both numbers are negative.
- According to rule 3, the quotient is positive.
- [tex]$0 \div -8.6$[/tex]:
- Zero divided by a negative number.
- According to rule 4, the quotient is zero, which is not considered negative.
Based on this 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.
