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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.

A. [tex]1.4 \div 99.9[/tex]
B. [tex]5.7 \div -2.2[/tex]
C. [tex]-0.01 \div 0.05[/tex]
D. [tex]-3 \div -0.009[/tex]
E. [tex]0 \div -8.6[/tex]

Answer :

To determine which expressions of signed decimal numbers have negative quotients, we will apply the rules of signed numbers:

1. Positive ÷ Positive = Positive
2. Positive ÷ Negative = Negative
3. Negative ÷ Positive = Negative
4. Negative ÷ Negative = Positive

We need to examine each expression:

1. [tex]\(1.4 \div 99.9\)[/tex]:
- A positive number (1.4) divided by a positive number (99.9).
- According to the rules, the quotient will be positive.

2. [tex]\(5.7 \div -2.2\)[/tex]:
- A positive number (5.7) divided by a negative number (-2.2).
- According to the rules, the quotient will be negative.

3. [tex]\(-0.01 \div 0.05\)[/tex]:
- A negative number (-0.01) divided by a positive number (0.05).
- According to the rules, the quotient will be negative.

4. [tex]\(-3 \div -0.009\)[/tex]:
- A negative number (-3) divided by a negative number (-0.009).
- According to the rules, the quotient will be positive.

5. [tex]\(0 \div -8.6\)[/tex]:
- Zero (0) divided by a negative number (-8.6).
- Dividing zero by any non-zero number results in zero, which is neither positive nor negative.

With this analysis, the expressions that result in a negative quotient are:

- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]

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