College

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]-0.01 \div 0.05[/tex]
- [tex]-3 \div -0.009[/tex]
- [tex]0 \div -8.6[/tex]

Answer :

To determine which expressions of signed decimal numbers have negative quotients, we need to follow the rules for dividing numbers with signs:

1. Positive ÷ Positive = Positive
2. Positive ÷ Negative = Negative
3. Negative ÷ Positive = Negative
4. Negative ÷ Negative = Positive
5. Zero divided by any non-zero number is Zero

Now, let's analyze each expression:

1. [tex]\(1.4 \div 99.9\)[/tex]:

Both numbers are positive, so the quotient will be positive.

2. [tex]\(5.7 \div -2.2\)[/tex]:

A positive number divided by a negative number results in a negative quotient.

3. [tex]\(-0.01 \div 0.05\)[/tex]:

A negative number divided by a positive number results in a negative quotient.

4. [tex]\(-3 \div -0.009\)[/tex]:

A negative number divided by another negative number results in a positive quotient.

5. [tex]\(0 \div -8.6\)[/tex]:

Dividing zero by a non-zero number gives zero, which is not negative or positive.

Based on the rules, the expressions that have negative quotients are:

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

These are the expressions that result in negative quotients.

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