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Answer :
To determine which expressions of signed decimal numbers have negative quotients, you need to evaluate the expressions based on the rules of division involving positive and negative numbers. Recall the following rules:
- A positive number divided by a positive number results in a positive quotient.
- A positive number divided by a negative number results in a negative quotient.
- A negative number divided by a positive number results in a negative quotient.
- A negative number divided by a negative number results in a positive quotient.
- Zero divided by any non-zero number results in zero, which is not negative.
Let's go through each expression:
1. [tex]\(1.4 \div 99.9\)[/tex]:
- Both numbers are positive.
- The quotient is positive.
2. [tex]\(5.7 \div -2.2\)[/tex]:
- The dividend (5.7) is positive and the divisor (-2.2) is negative.
- The quotient is negative.
3. [tex]\(-0.01 \div 0.05\)[/tex]:
- The dividend (-0.01) is negative and the divisor (0.05) is positive.
- The quotient is negative.
4. [tex]\(-3 \div -0.009\)[/tex]:
- Both numbers are negative.
- The quotient is positive.
5. [tex]\(0 \div -8.6\)[/tex]:
- Zero divided by any non-zero number is zero.
- Zero is not negative.
Based on these evaluations, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
These are the expressions where the quotients are negative.
- A positive number divided by a positive number results in a positive quotient.
- A positive number divided by a negative number results in a negative quotient.
- A negative number divided by a positive number results in a negative quotient.
- A negative number divided by a negative number results in a positive quotient.
- Zero divided by any non-zero number results in zero, which is not negative.
Let's go through each expression:
1. [tex]\(1.4 \div 99.9\)[/tex]:
- Both numbers are positive.
- The quotient is positive.
2. [tex]\(5.7 \div -2.2\)[/tex]:
- The dividend (5.7) is positive and the divisor (-2.2) is negative.
- The quotient is negative.
3. [tex]\(-0.01 \div 0.05\)[/tex]:
- The dividend (-0.01) is negative and the divisor (0.05) is positive.
- The quotient is negative.
4. [tex]\(-3 \div -0.009\)[/tex]:
- Both numbers are negative.
- The quotient is positive.
5. [tex]\(0 \div -8.6\)[/tex]:
- Zero divided by any non-zero number is zero.
- Zero is not negative.
Based on these evaluations, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
These are the expressions where the quotients are negative.
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