Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which expressions of signed decimal numbers have negative quotients? Check all that apply.

- [tex]1.4 \div 99.9[/tex]
- [tex]5.7 \div -2.2[/tex]
- [tex]-0.01 \div 0.05[/tex]
- [tex]-3 \div -0.009[/tex]
- [tex]0 \div -8.6[/tex]

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.