Answer :
To determine which expressions of signed decimal numbers have negative quotients, let's evaluate each expression one by one:
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- When you divide a positive number by another positive number, the quotient is positive.
- Quotient: Positive
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive and the second number is negative.
- Dividing a positive number by a negative number results in 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.
- Dividing a negative number by a positive number results in a negative quotient.
- Quotient: Negative
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- When you divide a negative number by another negative number, the quotient is positive.
- Quotient: Positive
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- Dividing zero by any non-zero number results in a quotient of zero.
- Zero is neither positive nor negative.
- Quotient: Neither positive nor negative (specifically zero)
Based on this evaluation, the expressions that result in negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
1. Expression: [tex]\(1.4 \div 99.9\)[/tex]
- Both numbers are positive.
- When you divide a positive number by another positive number, the quotient is positive.
- Quotient: Positive
2. Expression: [tex]\(5.7 \div -2.2\)[/tex]
- The first number is positive and the second number is negative.
- Dividing a positive number by a negative number results in 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.
- Dividing a negative number by a positive number results in a negative quotient.
- Quotient: Negative
4. Expression: [tex]\(-3 \div -0.009\)[/tex]
- Both numbers are negative.
- When you divide a negative number by another negative number, the quotient is positive.
- Quotient: Positive
5. Expression: [tex]\(0 \div -8.6\)[/tex]
- Dividing zero by any non-zero number results in a quotient of zero.
- Zero is neither positive nor negative.
- Quotient: Neither positive nor negative (specifically zero)
Based on this evaluation, the expressions that result in negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
