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Answer :
To determine which expressions of signed decimal numbers result in negative quotients, we need to look at the rules for dividing positive and negative numbers:
1. Positive ÷ Positive = Positive
2. Positive ÷ Negative = Negative
3. Negative ÷ Positive = Negative
4. Negative ÷ Negative = Positive
Let's analyze each expression:
1. [tex]\(1.4 \div 99.9\)[/tex]
- Both the dividend (1.4) and the divisor (99.9) are positive.
- This division results in a positive quotient.
2. [tex]\(5.7 \div -2.2\)[/tex]
- The dividend (5.7) is positive, and the divisor (-2.2) is negative.
- This division results in a negative quotient.
3. [tex]\(-0.01 \div 0.05\)[/tex]
- The dividend (-0.01) is negative, and the divisor (0.05) is positive.
- This division results in a negative quotient.
4. [tex]\(-3 \div -0.009\)[/tex]
- Both the dividend (-3) and the divisor (-0.009) are negative.
- This division results in a positive quotient.
5. [tex]\(0 \div -8.6\)[/tex]
- The dividend is 0, and the divisor (-8.6) is negative.
- Division of zero by any non-zero number results in a quotient of zero, which is neither positive nor negative.
Based on this analysis, the expressions that have negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
1. Positive ÷ Positive = Positive
2. Positive ÷ Negative = Negative
3. Negative ÷ Positive = Negative
4. Negative ÷ Negative = Positive
Let's analyze each expression:
1. [tex]\(1.4 \div 99.9\)[/tex]
- Both the dividend (1.4) and the divisor (99.9) are positive.
- This division results in a positive quotient.
2. [tex]\(5.7 \div -2.2\)[/tex]
- The dividend (5.7) is positive, and the divisor (-2.2) is negative.
- This division results in a negative quotient.
3. [tex]\(-0.01 \div 0.05\)[/tex]
- The dividend (-0.01) is negative, and the divisor (0.05) is positive.
- This division results in a negative quotient.
4. [tex]\(-3 \div -0.009\)[/tex]
- Both the dividend (-3) and the divisor (-0.009) are negative.
- This division results in a positive quotient.
5. [tex]\(0 \div -8.6\)[/tex]
- The dividend is 0, and the divisor (-8.6) is negative.
- Division of zero by any non-zero number results in a quotient of zero, which is neither positive nor negative.
Based on this analysis, the expressions that have negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
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