Answer :
Sure! Let's determine which expressions of signed decimal numbers have negative quotients by following a step-by-step approach. In division, a quotient is negative if one number is positive and the other number is negative. Let's examine each expression:
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- A positive number divided by a positive number gives a positive quotient.
- Quotient: Positive
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive, and the second number is negative.
- A positive divided by a negative gives a negative quotient.
- Quotient: Negative
3. Expression: [tex]\(-0.01 \div 0.05\)[/tex]
- The first number is negative, and the second number is positive.
- A negative divided by a positive gives a negative quotient.
- Quotient: Negative
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- A negative divided by a negative gives a positive quotient.
- Quotient: Positive
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- Any number divided by a non-zero number (when the numerator is zero) results in zero.
- Zero is not negative; it is neutral.
- Quotient: Not negative (zero)
Based on these evaluations, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
Therefore, the expressions with negative quotients are [tex]\(5.7 \div -2.2\)[/tex] and [tex]\(-0.01 \div 0.05\)[/tex].
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- A positive number divided by a positive number gives a positive quotient.
- Quotient: Positive
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive, and the second number is negative.
- A positive divided by a negative gives a negative quotient.
- Quotient: Negative
3. Expression: [tex]\(-0.01 \div 0.05\)[/tex]
- The first number is negative, and the second number is positive.
- A negative divided by a positive gives a negative quotient.
- Quotient: Negative
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- A negative divided by a negative gives a positive quotient.
- Quotient: Positive
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- Any number divided by a non-zero number (when the numerator is zero) results in zero.
- Zero is not negative; it is neutral.
- Quotient: Not negative (zero)
Based on these evaluations, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
Therefore, the expressions with negative quotients are [tex]\(5.7 \div -2.2\)[/tex] and [tex]\(-0.01 \div 0.05\)[/tex].
