This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. The expression with positive value is (-5)×(-3)=15, as two negatives make positive. A common error is picking one with odd negatives, like 5×(-3)=-15, thinking it's positive. To find positive, count negatives: even (two in C) → positive, odd → negative. Calculation steps help identify: determine sign by negative count, multiply magnitudes, apply sign.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. In this debt context, owing $5 per month is -5, times 6 months: 6×(-5)=-30, total debt of -$30. A common error is treating debt as positive to get $30, or arithmetic like 6+5=11. Count negatives: one (odd) means negative. Contexts like debt use negative amounts: 6×(-5)=-$30 total debt, avoiding mistakes like positive interpretation.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. Here, (2/3)×(3/4)= (2×3)/(3×4)=6/12, which simplifies to 1/2 by dividing numerator and denominator by 6. A common error is adding instead of multiplying, like (2+3)/(3+4)=5/7, or not simplifying 6/12. Since both are positive, the sign is positive; count negatives: zero (even) means positive. For calculation: (1) determine sign (even negatives → positive), (2) multiply magnitudes (numerators 2×3=6, denominators 3×4=12), (3) apply sign (6/12), (4) simplify (1/2), like scaling a quantity.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. For (-3)×(-5), both negative, so the rule gives positive: 15. A common error is treating negative times negative as negative, like (-3)×(-5)=-15, or miscalculating the magnitude as 3+5=8. To determine the sign, count the negatives: an even number (two here) means positive, odd means negative. For calculation: (1) determine sign (even negatives → positive), (2) multiply magnitudes (3×5=15), (3) apply sign (15), and in contexts like two debts canceling out to a gain.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. Here, (-1/2)×8 = - (1/2 × 8) = -4, applying the negative sign from the fraction. A common error is getting positive 4 by ignoring the sign, or wrong calculation like -8 or 1/16. Count negatives: one (odd) means negative. For calculation: (1) determine sign (odd → negative), (2) multiply magnitudes (1/2 × 8 = 4), (3) apply sign (-4), like reversing a quantity.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. Here, 6×(-4) involves a positive times a negative, so the result is negative: -24. A common error is forgetting the sign rule and getting 24 (positive), or miscalculating the magnitude like 6+4=10 or 6-4=2. To determine the sign, count the negatives: an odd number (one here) means negative, even means positive. For calculation: (1) determine sign (odd negatives → negative), (2) multiply magnitudes (6×4=24), (3) apply sign (-24), and consider contexts like scaling in the opposite direction.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. The statement (-4)×6=24 is false, because negative times positive is negative: -24. A common error is agreeing it's true by ignoring the sign, or thinking it's 0. Count negatives: one (odd) means negative, so product is -24, not 24. Use steps: (1) sign (odd → negative), (2) magnitudes (4×6=24), (3) apply sign (-24) to verify.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. For temperature drop of 3°C per hour (negative rate -3) over 4 hours: 4×(-3)=-12°C total change. A common error is using positive for drop to get 12°C, or wrong math like 4+3=7. Count negatives: one (odd) means negative. In temperature contexts, negative rate times time gives total drop: 4×(-3)=-12°C, avoiding positive misinterpretation.

This question tests multiplying rational numbers by applying sign rules (negative times negative is positive, positive times negative is negative) and interpreting products in contexts like debt or temperature changes. The sign rules are: positive times positive equals positive (like 3×5=15), negative times negative equals positive ((-3)×(-5)=15, since two negatives make a positive from properties like (-1)×(-1)=1), positive times negative equals negative (3×(-5)=-15), and negative times positive equals negative ((-3)×5=-15, due to commutativity). For fractions, multiply numerators and denominators, like (2/3)×(3/4)=6/12=1/2 simplified, and for decimals, multiply magnitudes and apply the sign, like (−2.5)×4 gives magnitudes 2.5×4=10, with negative×positive=negative, so -10. For (−2.5)×4, magnitudes 2.5×4=10, signs negative×positive=negative, result -10. A common error is ignoring the sign to get 10, or decimal mistakes like 2.5×4=1 or 100. To determine the sign, count the negatives: odd number (one) means negative. For calculation: (1) determine sign (odd → negative), (2) multiply magnitudes (2.5×4=10), (3) apply sign (-10), such as in contexts like negative scaling.

This question tests multiplying rational numbers mixing fractions and integers, with sign rules (negative $\times$ positive = negative). For $(- \frac{1}{2}) \times 8$: multiply as $- (\frac{1}{2}) \times 8 = -4$, or numerators $-1 \times 8 = -8$ over denominator 2, then $-8/2 = -4$. In context, like half in the opposite direction scaled by 8. Correctly, product is $-4$, not $4$ (wrong sign) or $-8$ (not simplifying) or $\frac{1}{16}$ (division error). Error like treating it as division or wrong fraction multiplication. Sign: one negative $\to$ negative. Calculation: sign $(-)$, magnitudes ($\frac{1}{2} \times 8 = 4$), apply $(-4)$; simplify if needed.