This question tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). Subtraction as addition: p-q=p+(-q) (7-4=7+(-4)=3, 5-(-2)=5+2=7 subtracting negative adds). Properties: rearrange (commutative: a+b=b+a), group (associative: (a+b)+c=a+(b+c)), strategically (47+3+(-18) group as (47+3)+(-18)=50-18=32 easier mental math). Fractions: common denominator (1/2+1/3=3/6+2/6=5/6). For example, calculate -8+15-5, rewrite: -8+15+(-5) (subtraction as addition), rearrange: 15+(-8)+(-5) (positive first), group negatives: 15+(-8-5)=15+(-13)=2; or fractions: 1/2-3/4=1/2+(-3/4)=2/4+(-3/4)=-1/4; or decimals: 5.2-(-1.5)=5.2+1.5=6.7. Here, rewrite -6-9 as -6+(-9), add magnitudes 6+9=15, keep negative sign to get -15. A common error is treating negative+negative as subtraction, like -6-9 as 6-9=-3, or forgetting the negative result to get 15. Process: (1) rewrite subtractions as additions (p-q→p+(-q), makes all same operation), (2) identify signs (which positive, which negative), (3) apply rules (same signs: add magnitudes keep sign, different signs: subtract magnitudes use larger's sign), (4) for fractions: common denominators first (1/2=3/6, 1/3=2/6, then add/subtract), (5) for mixed forms: convert to one type (decimals or fractions), (6) use properties strategically (rearrange to make easier: group round numbers, opposites). Strategic examples: -97+100-3=100+(-97)+(-3) group: 100+(-100)=0; or 27+(-18)+3=(27+3)+(-18)=30-18=12. Mistakes: sign errors most common, fraction operations without denominators, not using properties for efficiency, arithmetic errors tracking negatives.

This question tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive + positive (add magnitudes, positive result: $3+5=8$), negative + negative (add magnitudes, negative result: $-3 + (-5) = -8$), positive + negative or negative + positive (subtract smaller magnitude from larger, sign of larger: $8 + (-5) = 3$, $-8 + 5 = -3$). Subtraction as addition: $p - q = p + (-q)$ ($7 - 4 = 7 + (-4) = 3$, $5 - (-2) = 5 + 2 = 7$ subtracting negative adds). Properties: rearrange (commutative: $a + b = b + a$), group (associative: $(a + b) + c = a + (b + c)$), strategically ($47 + 3 + (-18)$ group as $(47 + 3) + (-18) = 50 - 18 = 32$ easier mental math). Fractions: common denominator ($\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$). For example, calculate $-8 + 15 - 5$, rewrite: $-8 + 15 + (-5)$ (subtraction as addition), rearrange: $15 + (-8) + (-5)$ (positive first), group negatives: $15 + (-8 - 5) = 15 + (-13) = 2$; or fractions: $\frac{1}{2} - \frac{3}{4} = \frac{1}{2} + (-\frac{3}{4}) = \frac{2}{4} + (-\frac{3}{4}) = -\frac{1}{4}$; or decimals: $5.2 - (-1.5) = 5.2 + 1.5 = 6.7$. Here, convert $-1.5 - \frac{3}{4}$ as $-1.5 + (-0.75) = -2.25$, or fractions: $-\frac{3}{2} - \frac{3}{4} = -\frac{6}{4} - \frac{3}{4} = -\frac{9}{4} = -2.25$. A common error is converting incorrectly, like $\frac{3}{4}$ as $0.34$ to get $-1.84$, or sign error to get $2.25$. Process: (1) rewrite subtractions as additions ($p - q \to p + (-q)$, makes all same operation), (2) identify signs (which positive, which negative), (3) apply rules (same signs: add magnitudes keep sign, different signs: subtract magnitudes use larger's sign), (4) for fractions: common denominators first ($\frac{1}{2} = \frac{3}{6}$, $\frac{1}{3} = \frac{2}{6}$, then add/subtract), (5) for mixed forms: convert to one type (decimals or fractions), (6) use properties strategically (rearrange to make easier: group round numbers, opposites). Strategic examples: $-97 + 100 - 3 = 100 + (-97) + (-3)$ group: $100 + (-100) = 0$; or $27 + (-18) + 3 = (27 + 3) + (-18) = 30 - 18 = 12$. Mistakes: sign errors most common, fraction operations without denominators, not using properties for efficiency, arithmetic errors tracking negatives.

This problem tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). For $5.2 - (-1.5)$, we apply the rule that subtracting a negative equals adding a positive: $5.2 - (-1.5) = 5.2 + 1.5$. Now we have positive+positive, so add magnitudes: $5.2 + 1.5 = 6.7$. A student might forget the double negative rule and compute $5.2 - 1.5 = 3.7$, or make a sign error. Process: (1) rewrite subtraction of negative as addition ($-(-1.5) = +1.5$), (2) identify signs (both positive), (3) apply rules (add magnitudes, keep positive), (4) calculate: 5.2+1.5=6.7.

This question tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). Subtraction as addition: p-q=p+(-q) (7-4=7+(-4)=3, 5-(-2)=5+2=7 subtracting negative adds). Properties: rearrange (commutative: a+b=b+a), group (associative: (a+b)+c=a+(b+c)), strategically (47+3+(-18) group as (47+3)+(-18)=50-18=32 easier mental math). Fractions: common denominator (1/2+1/3=3/6+2/6=5/6). For example, calculate -8+15-5, rewrite: -8+15+(-5) (subtraction as addition), rearrange: 15+(-8)+(-5) (positive first), group negatives: 15+(-8-5)=15+(-13)=2; or fractions: 1/2-3/4=1/2+(-3/4)=2/4+(-3/4)=-1/4; or decimals: 5.2-(-1.5)=5.2+1.5=6.7. Here, convert -1.5 - 3/4 as -1.5 + (-0.75) = -2.25, or fractions: -3/2 - 3/4 = -6/4 - 3/4 = -9/4 = -2.25. A common error is converting incorrectly, like 3/4 as 0.34 to get -1.84, or sign error to get 2.25. Process: (1) rewrite subtractions as additions (p-q→p+(-q), makes all same operation), (2) identify signs (which positive, which negative), (3) apply rules (same signs: add magnitudes keep sign, different signs: subtract magnitudes use larger's sign), (4) for fractions: common denominators first (1/2=3/6, 1/3=2/6, then add/subtract), (5) for mixed forms: convert to one type (decimals or fractions), (6) use properties strategically (rearrange to make easier: group round numbers, opposites). Strategic examples: -97+100-3=100+(-97)+(-3) group: 100+(-100)=0; or 27+(-18)+3=(27+3)+(-18)=30-18=12. Mistakes: sign errors most common, fraction operations without denominators, not using properties for efficiency, arithmetic errors tracking negatives.

This question tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). Subtraction as addition: p-q=p+(-q) (7-4=7+(-4)=3, 5-(-2)=5+2=7 subtracting negative adds). Properties: rearrange (commutative: a+b=b+a), group (associative: (a+b)+c=a+(b+c)), strategically (47+3+(-18) group as (47+3)+(-18)=50-18=32 easier mental math). Fractions: common denominator (1/2+1/3=3/6+2/6=5/6). For example, calculate -8+15-5, rewrite: -8+15+(-5) (subtraction as addition), rearrange: 15+(-8)+(-5) (positive first), group negatives: 15+(-8-5)=15+(-13)=2; or fractions: 1/2-3/4=1/2+(-3/4)=2/4+(-3/4)=-1/4; or decimals: 5.2-(-1.5)=5.2+1.5=6.7. Here, add -3.5 + 2.8: subtract magnitudes 3.5-2.8=0.7, sign of larger (-3.5) gives -0.7. A common error is sign confusion, like adding as positive to get 6.3, or reversing signs to get 0.7. Process: (1) rewrite subtractions as additions (p-q→p+(-q), makes all same operation), (2) identify signs (which positive, which negative), (3) apply rules (same signs: add magnitudes keep sign, different signs: subtract magnitudes use larger's sign), (4) for fractions: common denominators first (1/2=3/6, 1/3=2/6, then add/subtract), (5) for mixed forms: convert to one type (decimals or fractions), (6) use properties strategically (rearrange to make easier: group round numbers, opposites). Strategic examples: -97+100-3=100+(-97)+(-3) group: 100+(-100)=0; or 27+(-18)+3=(27+3)+(-18)=30-18=12. Mistakes: sign errors most common, fraction operations without denominators, not using properties for efficiency, arithmetic errors tracking negatives.

This problem tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: $3+5=8$), negative+negative (add magnitudes, negative result: $-3 + (-5) = -8$), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: $8 + (-5) = 3$, $-8 + 5 = -3$). For $\frac{1}{2} + (-\frac{3}{4})$, we need a common denominator: $\frac{1}{2} = \frac{2}{4}$. Now we have $\frac{2}{4} + (-\frac{3}{4})$, which is positive+negative with different signs. We subtract the smaller magnitude from the larger: $\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$, and since $\frac{3}{4} > \frac{2}{4}$ and the larger term is negative, the result is $-\frac{1}{4}$. A student might forget to find a common denominator and incorrectly compute $\frac{1}{2} + (-\frac{3}{4}) = -\frac{2}{6}$ or make a sign error. Process: (1) find common denominator (4), (2) convert fractions ($\frac{1}{2} = \frac{2}{4}$), (3) identify signs (positive+negative), (4) apply rules (subtract magnitudes, use sign of larger), (5) calculate: $\frac{2}{4} - \frac{3}{4} = -\frac{1}{4}$.

This problem tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). For $-3.5 + 2.8$, we have negative+positive with different signs. Subtract the smaller magnitude from the larger: $3.5 - 2.8 = 0.7$. Since $|-3.5| > |2.8|$ and the larger magnitude is negative, the result is $-0.7$. A student might incorrectly add the magnitudes to get 6.3 or -6.3, or make a subtraction error. Process: (1) identify signs (negative+positive), (2) find magnitudes (3.5 and 2.8), (3) apply rules (subtract smaller from larger magnitude), (4) determine sign (larger magnitude was negative), (5) calculate: 3.5-2.8=0.7, so answer is -0.7.

This question tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). Subtraction as addition: p-q=p+(-q) (7-4=7+(-4)=3, 5-(-2)=5+2=7 subtracting negative adds). Properties: rearrange (commutative: a+b=b+a), group (associative: (a+b)+c=a+(b+c)), strategically (47+3+(-18) group as (47+3)+(-18)=50-18=32 easier mental math). Fractions: common denominator (1/2+1/3=3/6+2/6=5/6). For example, calculate -8+15-5, rewrite: -8+15+(-5) (subtraction as addition), rearrange: 15+(-8)+(-5) (positive first), group negatives: 15+(-8-5)=15+(-13)=2; or fractions: 1/2-3/4=1/2+(-3/4)=2/4+(-3/4)=-1/4; or decimals: 5.2-(-1.5)=5.2+1.5=6.7. Here, rewrite 12-(-5) as 12+5, then add to get 17, noting subtracting a negative is adding the positive. A common error is mishandling the double negative, like treating -(-5) as -5 to get 12-5=7, or sign confusion leading to -17. Process: (1) rewrite subtractions as additions (p-q→p+(-q), makes all same operation), (2) identify signs (which positive, which negative), (3) apply rules (same signs: add magnitudes keep sign, different signs: subtract magnitudes use larger's sign), (4) for fractions: common denominators first (1/2=3/6, 1/3=2/6, then add/subtract), (5) for mixed forms: convert to one type (decimals or fractions), (6) use properties strategically (rearrange to make easier: group round numbers, opposites). Strategic examples: -97+100-3=100+(-97)+(-3) group: 100+(-100)=0; or 27+(-18)+3=(27+3)+(-18)=30-18=12. Mistakes: sign errors most common, fraction operations without denominators, not using properties for efficiency, arithmetic errors tracking negatives.

This problem tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). For $-1.5 - \frac{3}{4}$, first rewrite as addition: $-1.5 + (-\frac{3}{4})$. Convert $\frac{3}{4}$ to decimal: $\frac{3}{4} = 0.75$. Now we have $-1.5 + (-0.75)$, which is negative+negative. Add magnitudes: $1.5 + 0.75 = 2.25$, and keep the negative sign: $-2.25$. A student might make a conversion error ($\frac{3}{4} \neq 0.75$) or a sign error. Process: (1) rewrite subtraction as addition, (2) convert to common form ($\frac{3}{4} = 0.75$), (3) identify signs (both negative), (4) apply rules (add magnitudes, keep negative), (5) calculate: $1.5 + 0.75 = 2.25$, so answer is $-2.25$.

This problem tests adding and subtracting rational numbers (integers, fractions, decimals, positive/negative) using properties of operations strategically. Sign rules: positive+positive (add magnitudes, positive result: 3+5=8), negative+negative (add magnitudes, negative result: -3+(-5)=-8), positive+negative or negative+positive (subtract smaller magnitude from larger, sign of larger: 8+(-5)=3, -8+5=-3). For $47 + (-18) + 3$, we can use the commutative property to rearrange as $47 + 3 + (-18)$, then use the associative property to group as $(47 + 3) + (-18) = 50 + (-18)$. Since we have positive+negative with different signs, we subtract magnitudes: $50 - 18 = 32$, and since 50 > 18, the result is positive: $32$. A student might incorrectly add all magnitudes getting 68, or make a sign error getting -32, but the correct answer using strategic grouping is 32. Process: (1) rewrite subtractions as additions (already done), (2) identify signs (47 positive, -18 negative, 3 positive), (3) rearrange strategically to make mental math easier (group 47+3=50), (4) apply rules (50+(-18) means subtract 18 from 50), (5) verify: 50-18=32.