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------------------------------------------------ Applying the Rules of Signed Numbers to Decimals

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]-3 \div -0.009[/tex]

To determine which expressions of signed decimal numbers have negative quotients, we need to consider the rules for dividing positives and negatives:

1. A positive number divided by a positive number results in a positive quotient.
2. A positive number divided by a negative number results in a negative quotient.
3. A negative number divided by a positive number results in a negative quotient.
4. A negative number divided by a negative number results in a positive quotient.
5. Any number divided by zero is undefined, and zero divided by any number (except zero) is zero.

Now, let's examine each expression:

1. [tex]$1.4 \div 99.9$[/tex]:
- Dividing a positive number by a positive number.
- The quotient is positive.

2. [tex]$5.7 \div -2.2$[/tex]:
- Dividing a positive number by a negative number.
- The quotient is negative.

3. [tex]$-0.01 + 0.05$[/tex]:
- This is an addition operation, not division.
- It doesn't apply to the question of quotients.

4. [tex]$-3 \div -0.009$[/tex]:
- Dividing a negative number by a negative number.
- The quotient is positive.

5. [tex]$0 \div -8.6$[/tex]:
- Dividing zero by a negative number.
- The quotient is zero (which is not negative).

From the options given, the expression that results in a negative quotient is:

- [tex]$5.7 \div -2.2$[/tex]

Therefore, the expression with a negative quotient is [tex]$5.7 \div -2.2$[/tex].