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Answer :
We need to check the sign of the result (known as the quotient) for each division expression. Recall that when dividing two numbers:
- If both numbers have the same sign (both positive or both negative), the quotient is positive.
- If the numbers have opposite signs (one positive and one negative), the quotient is negative.
- Division by any nonzero number of zero gives 0, which is neither positive nor negative.
Let’s examine the expressions:
1. For
[tex]$$1.4 \div 99.9,$$[/tex]
both [tex]$1.4$[/tex] and [tex]$99.9$[/tex] are positive. Therefore, the quotient is positive.
2. For
[tex]$$5.7 \div -2.2,$$[/tex]
[tex]$5.7$[/tex] is positive and [tex]$-2.2$[/tex] is negative. Since they have opposite signs, the quotient is negative.
3. For
[tex]$$-0.01 \div 0.05,$$[/tex]
[tex]$-0.01$[/tex] is negative and [tex]$0.05$[/tex] is positive. Again, they have opposite signs, so the quotient is negative.
4. The expression
[tex]$$-3 + -0.009$$[/tex]
is an addition, not a division, so it is not considered in this problem.
5. For
[tex]$$0 \div -8.6,$$[/tex]
the numerator is [tex]$0$[/tex]. The value of this expression is [tex]$0$[/tex], which is neither positive nor negative.
Thus, the expressions that yield negative quotients are the ones in parts 2 and 3.
The final answer is: Expression 2 and Expression 3.
- If both numbers have the same sign (both positive or both negative), the quotient is positive.
- If the numbers have opposite signs (one positive and one negative), the quotient is negative.
- Division by any nonzero number of zero gives 0, which is neither positive nor negative.
Let’s examine the expressions:
1. For
[tex]$$1.4 \div 99.9,$$[/tex]
both [tex]$1.4$[/tex] and [tex]$99.9$[/tex] are positive. Therefore, the quotient is positive.
2. For
[tex]$$5.7 \div -2.2,$$[/tex]
[tex]$5.7$[/tex] is positive and [tex]$-2.2$[/tex] is negative. Since they have opposite signs, the quotient is negative.
3. For
[tex]$$-0.01 \div 0.05,$$[/tex]
[tex]$-0.01$[/tex] is negative and [tex]$0.05$[/tex] is positive. Again, they have opposite signs, so the quotient is negative.
4. The expression
[tex]$$-3 + -0.009$$[/tex]
is an addition, not a division, so it is not considered in this problem.
5. For
[tex]$$0 \div -8.6,$$[/tex]
the numerator is [tex]$0$[/tex]. The value of this expression is [tex]$0$[/tex], which is neither positive nor negative.
Thus, the expressions that yield negative quotients are the ones in parts 2 and 3.
The final answer is: Expression 2 and Expression 3.
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