This question tests multiplying rational numbers with decimals, applying sign rules ($negative \times positive = negative$) and calculating accurately. Decimals: multiply magnitudes, apply sign; $(-2.5) \times 4$: magnitudes $2.5 \times 4 = 10$, signs $negative \times positive = negative$, result $-10$. For example, scaling a negative value by a positive factor keeps the negative direction. Correctly, it's $-10$, not $10$ (ignoring sign) or $-1$/-$100$ (arithmetic errors). A common mistake is decimal placement error, like thinking $2.5 \times 4 = 1$ or $100$. Sign: one negative → odd, so negative. Steps: sign (odd negatives → -), magnitudes ($2.5 \times 4 = 10$), apply ($-10$).

This question tests multiplying rational numbers in a temperature context, where drop is negative, applying sign rules (positive hours × negative per hour = negative total). So, 4 × (-3) = -12°C, meaning a total drop of 12°C over 4 hours. Context: temperature drop as negative rate, positive time yields negative change. Correctly, -12°C, not 12°C (wrong sign) or -7°C (math error). Mistake like adding rates instead of multiplying. Sign: odd negatives → negative. Calculation: sign (-), magnitudes (4 × 3 = 12), apply (-12°C); contexts like this show real-world application.

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.

This question tests verifying a multiplication of rational numbers using sign rules, where positive times negative equals negative. The sign rules state that positive × positive = positive (e.g., 3×5=15), negative × negative = positive (e.g., (-3)×(-5)=15), positive × negative = negative (e.g., 3×(-5)=-15), and negative × positive = negative (e.g., (-3)×5=-15). For example, 5×(-3)=-15, as positive × negative = negative, with magnitude 5×3=15. The statement is true because positive × negative is negative, and 5×3=15 leads to -15. A common error is claiming positive × negative = positive, or wrong magnitude like 5×3=8. Calculation: (1) sign (odd negatives → negative), (2) magnitudes (5×3=15), (3) apply sign (-15). Avoid sign rule errors or arithmetic mistakes in verification.

This question tests multiplying rational numbers as negative and positive fractions, applying sign rules and simplifying. Multiply: (-2/3) × (3/5) = (-2×3)/(3×5) = -6/15, simplify by dividing by 3 to -2/5. Sign rules: negative × positive = negative, with fraction multiplication of numerators and denominators. Correctly, -2/5, not -6/15 (unsimplified) or positive versions (sign error) or 6/8 (wrong math). Error like multiplying denominators wrong or ignoring sign. Sign: one negative → negative. Steps: sign (-), magnitudes (2/3 × 3/5 = 6/15 = 2/5), apply (-2/5), simplify.

This question tests multiplying rational numbers by applying sign rules, where a positive times a negative equals a negative, and interpreting products in contexts like scaling or debt. The sign rules state that positive × negative = negative, as in 6 × (-4) where the positive 6 and negative -4 result in a negative product. For example, if you have a rate of -4 units per step and take 6 steps, the total is -24 units, representing a loss or decrease. Here, multiplying the magnitudes 6 × 4 = 24 and applying the negative sign from the one negative factor gives -24. A common error is ignoring the sign and choosing 24, or miscalculating the magnitude like 6 × 4 = 10 or 20. To determine the sign, count the negatives: one negative means odd number, so negative result. Always multiply magnitudes first, apply the sign, and verify in context, such as a positive time period times a negative rate yielding a negative total change.

This question tests multiplying rational numbers by applying sign rules, where negative times negative equals positive, and interpreting products in contexts like debt or temperature changes. The sign rules state that positive × positive = positive (e.g., 3×5=15), negative × negative = positive (e.g., (-3)×(-5)=15, as two negatives make positive from properties like (-1)×(-1)=1), positive × negative = negative (e.g., 3×(-5)=-15), and negative × positive = negative (e.g., (-3)×5=-15, due to commutativity). For example, (-3)×(-5) both negative, so the rule gives positive: 15. In this case, the correct calculation is (-3)×(-5)=15, as the magnitude 3×5=15 takes a positive sign from the two negatives. A common error is applying negative × negative = negative, like (-3)×(-5)=-15, or misadding like -3 + -5 = -8. To determine the sign, count the negatives: here, an even number (two) leads to positive, while odd would be negative, like (-3)×5=-15. For calculation: (1) determine sign (even negatives → positive), (2) multiply magnitudes (3×5=15), (3) apply sign (15), and avoid mistakes like wrong sign rules or arithmetic errors.

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. 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 applying sign rules, specifically negative × negative = positive, and understanding products in contexts like double reversals. Sign rules: negative × negative = positive, as (-3) × (-5) = 15, since two negatives make a positive from properties like (-1) × (-1) = 1. For example, (-3) × (-5) both negative, so the rule gives positive 15; in context, like reversing a debt twice. Correctly, multiply magnitudes 3 × 5 = 15 and apply positive sign due to even number of negatives. A common mistake is treating negative × negative as negative, resulting in -15. Sign determination: count negatives (even number → positive). Calculation steps: determine sign (even negatives → +), multiply magnitudes (3 × 5 = 15), apply sign (+15).