This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For division, move the decimal in the divisor right to make it whole (1.2→12, 1 place), move the dividend the same (15.6→156), then divide as whole numbers (156÷12=13); addition and subtraction align decimals; multiplication counts places. For example, 15.6÷1.2: shift to 156÷12=13. The correct amount per batch is 15.6 ÷ 1.2 = 13 cups, which is choice C. A common error is not moving decimals in both, leading to 1.3 or 0.13, or arithmetic mistakes like 156÷12=12 resulting in 1.2. Standard algorithms for division: shift decimals right equally, divide as whole numbers, place decimal in quotient if needed. Verification by multiplication, like 13 × 1.2 = 15.6, confirms; this is useful in recipes and sharing quantities.

This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For subtraction, align decimal points vertically, such as 45.60 over 12.75, and subtract columns from right to left, borrowing as needed; addition follows similar alignment; multiplication ignores decimals first, then counts places; division shifts decimals to whole numbers. For example, subtracting 45.60 - 12.75: align as 45.60 and 12.75, hundredths 0-5 requires borrowing (10-5=5, tenths become 5), tenths 5-7 requires borrowing (15-7=8, units become 4), units 4-2=2, tens 4-1=3, resulting in 32.85. The correct amount used is 45.60 - 12.75 = 32.85 ounces, which is choice A. A common error is improper borrowing, such as not adjusting for decimals leading to 33.15 or 32.95, or misalignment causing 3.285. Standard algorithms ensure precision: align decimals, subtract with borrowing, and keep the decimal in place. Verification via addition, like 32.85 + 12.75 = 45.60, confirms the result; this applies to measurements like tracking fluid ounces.

This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For subtraction, align decimals, writing 72.08 - 19.60, and subtract with borrowing; addition aligns for carrying; multiplication counts places; division shifts to whole. For example, 72.08 - 19.60: align, hundredths 8-0=8, tenths 0-6 requires borrowing (10-6=4, units 1 becomes 0, but from 2), actually full: borrow across, resulting in 52.48. The correct remaining solution is 72.08 - 19.6 = 52.48 mL, which is choice A. A common error is borrowing mistakes, leading to 53.48 or 51.48, or misalignment like 524.8. Standard algorithms: align, subtract with borrowing, decimal in place. Verification by addition, 52.48 + 19.6 = 72.08, confirms; used in science for volumes.

This question tests fluently adding, subtracting, multiplying, and dividing multi-digit decimals using standard algorithms: align decimal points for addition and subtraction, count decimal places for multiplication, and move decimals to make the divisor whole for division. For multiplication, ignore decimals and multiply as whole numbers (3.5 as 35, 2.4 as 24, 35×24=840), then count total decimal places (1+1=2) and place the decimal accordingly (8.40 or 8.4); addition and subtraction align decimals; division shifts to whole numbers. For example, 3.5×2.4: 35×24=840, with 2 decimal places, becomes 8.40=8.4. The correct area is 3.5 × 2.4 = 8.4 square inches, which is choice C. A common error is incorrect decimal placement, such as using 1 place to get 84.0 or 3 places for 0.84, or arithmetic errors like 35×24=800 leading to 8.00. Standard algorithms for multiplication: ignore decimals, multiply, count places, insert decimal from the right. Verification by division, like 8.4 ÷ 2.4 = 3.5, confirms; this applies to areas and measurements.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, multiply 2.75 × 3 as 275 × 3 = 825, with 2 decimal places, so 8.25. A common error is forgetting decimal places, resulting in 825 or 0.825. Standard algorithms facilitate scaling in recipes, verifiable by division, preventing placement errors.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (45.60 over 12.75, decimals line up), add/subtract columns right to left (0-5 can't borrow to 10-5=5, 5-7 can't borrow to 15-7=8 with carryover effects, resulting in 32.85), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this subtraction, align 45.60 and 12.75, subtract with borrowing to get 32.85 ounces drunk. A common error is misalignment or improper borrowing, like subtracting without borrow leading to 32.95 or arithmetic mistakes. Standard algorithms: subtract with alignment and regrouping; verification by adding back (32.85 + 12.75 = 45.60 checks out). In measurement contexts like ounces, this ensures precise calculations.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (67.08 over 9.45, decimals line up), add/subtract columns right to left (8+5=13 write 3 carry 1, 0+4+1=5, 7+9=16 write 6 carry 1, 6+0+1=7: sum 76.53), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this addition, align 67.08 and 9.45, add to get 76.53. A common error is not aligning, like adding as 6708+945=7653 without decimal, or carry mistake like 76.513. Standard algorithms ensure precision: align and add with carry; verification by subtraction (76.53 - 9.45 = 67.08 checks out). Mistakes often involve alignment or arithmetic.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this division, move decimals one place to get 156÷12=13. A common error is not moving decimals in both, like 15.6÷1.2 as 156÷12 misplaced or arithmetic error like 130. Standard algorithms: move decimals equally then divide; verification by multiplication (13 × 1.2 = 15.6 checks out). In rate contexts like kilometers per hour, this ensures accuracy.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (24.60 over 7.85, decimals line up), add/subtract columns right to left (0-5 can't borrow to 10-5=5, then further borrowing leading to 16.75), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this subtraction, write 24.6 as 24.60, align with 7.85, subtract with borrowing to get 16.75. A common error is insufficient borrowing, like 17.75 or misalignment as 16.85. Standard algorithms: pad zeros for alignment and subtract; verification by addition (16.75 + 7.85 = 24.60 checks out). Mistakes include regrouping errors in subtraction.

This question tests fluently adding, subtracting, multiplying, dividing multi-digit decimals using standard algorithms: align decimal points (add/subtract), count decimal places (multiply), move decimals to make whole (divide). Addition/Subtraction: align decimal points vertically (12.50 over 3.75, decimals line up), add/subtract columns right to left (5+5=10 carry, 2+7=9, 1+3=4, 0+0=0: sum 16.25), decimal in answer below operands. Multiplication: multiply ignoring decimals (3.5×2.4→35×24=840), count total decimal places in factors (3.5 has 1, 2.4 has 1, total 2), place decimal in product from right (840 with 2 places: 8.40=8.4). Division: move divisor decimal right making whole (1.2→12 move 1 place), move dividend same amount (15.6→156), divide as whole numbers (156÷12=13). For this question, add 18.45 + 7.80 by aligning decimals: 18.45 + 7.80 = 26.25. A common error is misalignment, such as adding without carrying over, resulting in 25.25. Standard algorithms: add/subtract (align decimals, operate, decimal below), multiply (ignore decimals, multiply, count places, insert decimal), divide (move decimals right, divide, quotient has decimal); verification and contexts like tracking distances help avoid mistakes like forgetting to carry.