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 (2.5→25 move 1 place), move dividend same amount (48.75→487.5), divide as whole numbers (487.5÷25=19.5). For this division, move decimals one place to get 487.5÷25=19.5 ounces per serving. A common error is moving decimals incorrectly, like 48.75÷2.5 as 1.95 or 195 without adjustment. Standard algorithms: equal decimal moves then divide; verification by multiplication (19.5 × 2.5 = 48.75 checks out). In recipe contexts, this avoids portion errors.

Perimeter = 2(length + width) = 2(12.8 + 9.45) = 2(22.25) = 44.5 meters. Cost = 44.5 × $7.50 = $333.75. Choice B is half the correct answer (forgetting to double for both lengths and widths). Choice C is double the correct answer. Choice D results from calculating area instead of perimeter.

First, calculate flour needed for 1.5 times the recipe: 2.75 × 1.5 = 4.125 cups. Then find how much more is needed: 4.125 - 3.8 = 0.325 cups. Choice B results from calculating 2.75 + 1.5 - 3.8 instead of multiplying. Choice C comes from miscalculating 2.75 × 1.5 as 3.025. Choice D results from adding instead of subtracting: 4.125 - 3.8 calculated incorrectly.

When you encounter a multi-step word problem like this, break it down into separate calculations based on what information you're given and what you need to find.

You have three key pieces of information: Emma's car gets 28.4 miles per gallon, she used 15.75 gallons, and gas costs $3.89 per gallon. You need to find both the total distance and total cost.

For distance traveled, multiply miles per gallon by gallons used: $$28.4 \times 15.75 = 447.3$$ miles. For the cost of gas, multiply gallons used by price per gallon: $$15.75 \times 3.89 = 61.27$$ dollars.

Looking at the wrong answers: Choice A uses an incorrect distance calculation of 462.8 miles, which suggests an error in multiplication, and also has the wrong gas cost. Choice B has the wrong distance (437.1 miles) but happens to get the correct gas cost—this shows someone made an arithmetic error on the first part but calculated the second part correctly. Choice C gets the distance right (447.3 miles) but calculates the gas cost incorrectly as $67.52, possibly by making an error in decimal multiplication.

Choice D correctly shows 447.3 miles traveled and $61.27 spent on gas.

Study tip: In multi-step problems, solve each part independently and double-check your decimal multiplication. Many mistakes happen when rushing through the arithmetic, so take time to line up decimal places correctly when multiplying.

When you encounter unit rate problems like this, you need to find the cost per unit for each option, then compare them. This question asks for the difference in price per dozen cupcakes between box sizes.

First, calculate the price per dozen for small boxes: $$\frac{\24.75}{8.25 \text{ dozen}} = \3.00$$ per dozen. Next, find the price per dozen for large boxes: $$\frac{\35.50}{12.5 \text{ dozen}} = \2.84$$ per dozen. The difference is $$\3.00 - \2.84 = \0.16$$ per dozen, making choice B correct.

Let's examine why the other answers are wrong. Choice A ($0.26) might result from calculation errors when dividing the costs by the quantities. Choice C ($0.84) could come from mistakenly subtracting $2.84 from $3.68 (if you incorrectly calculated one of the unit rates) or from other computational mistakes. Choice D ($0.58) might arise from errors in the division process or mixing up which values to subtract.

The key insight here is that large boxes offer a better deal per dozen cupcakes, which makes economic sense since bulk purchases typically cost less per unit.

Study tip: For unit rate comparison problems, always set up your fractions as $$\frac{\text{total cost}}{\text{total quantity}}$$ for each option, calculate carefully, then find the difference. Double-check your division by ensuring your unit rates make sense - larger quantities usually mean lower per-unit costs.

This is a constant rate problem, which means you need to find how fast water flows per hour, then use that rate to calculate the total after a different amount of time.

First, find the rate of water flow. Since the pool contains 847.5 gallons after 2.5 hours of constant filling, divide the total gallons by the time: $$847.5 ÷ 2.5 = 339$$ gallons per hour.

Now multiply this rate by the new time period: $$339 × 6.25 = 2,118.75$$ gallons. This confirms answer C is correct.

Let's examine why the other answers are wrong. Answer A (1,983.25 gallons) comes from incorrectly calculating the rate as 339 gallons per hour but then multiplying by 5.85 hours instead of 6.25 hours. Answer B (2,227.50 gallons) results from using an incorrect rate of 356.4 gallons per hour, possibly from a calculation error when dividing 847.5 by 2.5. Answer D (2,039.06 gallons) appears to stem from multiple computational mistakes, likely involving both an incorrect rate calculation and improper multiplication.

When solving constant rate problems, always follow this two-step process: first find the unit rate (divide total amount by time), then multiply that rate by the new time period. Double-check your division and multiplication, especially with decimals, as small calculation errors can lead you to attractive but incorrect answer choices.

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.