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Answer :
To determine which expressions have negative quotients, we need to look at the signs of the numbers in each division operation. A quotient is negative when one number is positive and the other number is negative. Let's analyze each of the given expressions:
1. [tex]\(1.4 \div 99.9\)[/tex]:
- Here, both numbers (1.4 and 99.9) are positive.
- The quotient will be positive.
2. [tex]\(5.7 \div -2.2\)[/tex]:
- The first number, 5.7, is positive, and the second number, -2.2, is negative.
- A positive number divided by a negative number results in a negative quotient.
3. [tex]\(-0.01 \div 0.05\)[/tex]:
- The first number, -0.01, is negative, and the second number, 0.05, is positive.
- A negative number divided by a positive number results in a negative quotient.
4. [tex]\(-3 \div -0.009\)[/tex]:
- Both numbers are negative (-3 and -0.009).
- Dividing a negative number by another negative number results in a positive quotient.
5. [tex]\(0+-8.6\)[/tex]:
- This is not a division operation; it's an addition operation.
- The expression simplifies to -8.6, which is negative, but it is not a quotient.
Based on this analysis, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
These are the expressions that yield negative quotients.
1. [tex]\(1.4 \div 99.9\)[/tex]:
- Here, both numbers (1.4 and 99.9) are positive.
- The quotient will be positive.
2. [tex]\(5.7 \div -2.2\)[/tex]:
- The first number, 5.7, is positive, and the second number, -2.2, is negative.
- A positive number divided by a negative number results in a negative quotient.
3. [tex]\(-0.01 \div 0.05\)[/tex]:
- The first number, -0.01, is negative, and the second number, 0.05, is positive.
- A negative number divided by a positive number results in a negative quotient.
4. [tex]\(-3 \div -0.009\)[/tex]:
- Both numbers are negative (-3 and -0.009).
- Dividing a negative number by another negative number results in a positive quotient.
5. [tex]\(0+-8.6\)[/tex]:
- This is not a division operation; it's an addition operation.
- The expression simplifies to -8.6, which is negative, but it is not a quotient.
Based on this analysis, the expressions with negative quotients are:
- [tex]\(5.7 \div -2.2\)[/tex]
- [tex]\(-0.01 \div 0.05\)[/tex]
These are the expressions that yield negative quotients.
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