To find the remaining amount of paint, subtract the amount used from the starting amount: \(7\frac{1}{8} - 2\frac{3}{4}\). First, find a common denominator, which is 8. The problem becomes \(7\frac{1}{8} - 2\frac{6}{8}\). Since \(\frac{1}{8}\) is smaller than \(\frac{6}{8}\), you need to regroup from the 7. Borrow 1 from 7, making it 6. Add the borrowed 1 (as \(\frac{8}{8}\)) to the fraction: \(\frac{1}{8} + \frac{8}{8} = \frac{9}{8}\). The problem is now \(6\frac{9}{8} - 2\frac{6}{8} = 4\frac{3}{8}\) gallons.

First, find the total length of the two pieces cut off: \(4\frac{1}{3} + 5\frac{1}{2}\). The common denominator is 6. \(4\frac{2}{6} + 5\frac{3}{6} = 9\frac{5}{6}\) feet. Next, subtract this total from the original length of the plank: \(12 - 9\frac{5}{6}\). Regroup 12 as \(11\frac{6}{6}\). Then, \(11\frac{6}{6} - 9\frac{5}{6} = 2\frac{1}{6}\) feet.

First, find the combined thickness of the math and science books: \(2\frac{1}{2} + 3\frac{1}{8}\). The common denominator is 8. \(2\frac{4}{8} + 3\frac{1}{8} = 5\frac{5}{8}\) inches. Next, subtract this combined thickness from the total height of the stack: \(8\frac{1}{4} - 5\frac{5}{8}\). The common denominator is 8. \(8\frac{2}{8} - 5\frac{5}{8}\). Regroup from the 8: \(7\frac{10}{8} - 5\frac{5}{8} = 2\frac{5}{8}\) inches.

This is a multi-step word problem involving mixed numbers and subtraction. When you see a problem asking "how much is left over," you need to find the difference between what was bought and what was used.

First, calculate how much fabric Sara actually needs by adding the blue and silver fabric requirements: $$2\frac{1}{2} + 1\frac{3}{4}$$. To add mixed numbers, convert them to improper fractions or find a common denominator. Using common denominators: $$2\frac{2}{4} + 1\frac{3}{4} = 3\frac{5}{4} = 4\frac{1}{4}$$ yards total needed.

Next, subtract the amount needed from the amount bought: $$5 - 4\frac{1}{4} = 4\frac{4}{4} - 4\frac{1}{4} = \frac{3}{4}$$ yard left over.

Looking at the wrong answers: Choice A ($$2\frac{1}{2}$$ yards) might come from subtracting only one fabric type instead of both. Choice B ($$1\frac{1}{4}$$ yards) could result from calculation errors when working with the mixed numbers or adding instead of subtracting somewhere in the process. Choice D ($$4\frac{1}{4}$$ yards) is actually the total amount of fabric Sara needs, not the leftover amount—this represents confusing what the question is asking for.

The correct answer is C: $$\frac{3}{4}$$ yard.

Study tip: In word problems involving "left over" or "remaining," always identify what you start with, subtract what you use, and double-check that your answer makes logical sense. Practice converting between mixed numbers and improper fractions to avoid calculation errors.

This problem requires subtracting the final amount of gas from the amount present before refueling. First, find the amount of gas in the tank before adding more, which was \(\frac{1}{4}\) full. The owner filled it to \(\frac{2}{3}\) full. The amount added is the difference: \(\frac{2}{3} - \frac{1}{4}\). The common denominator is 12. \(\frac{8}{12} - \frac{3}{12} = \frac{5}{12}\). The starting amount of \(\frac{7}{8}\) full is extra information not needed to solve for the amount added.

First, find the total amount of flour used by adding the two amounts: \(3\frac{1}{2} + 2\frac{1}{4}\). Find a common denominator for 2 and 4, which is 4. \(3\frac{2}{4} + 2\frac{1}{4} = 5\frac{3}{4}\) pounds. Next, subtract the total amount used from the initial amount: \(10 - 5\frac{3}{4}\). To subtract, regroup 10 as \(9\frac{4}{4}\). So, \(9\frac{4}{4} - 5\frac{3}{4} = 4\frac{1}{4}\) pounds.

Subtract the amount of water remaining from the initial amount: \(4\frac{1}{4} - 2\frac{2}{3}\). The least common denominator for 4 and 3 is 12. The problem becomes \(4\frac{3}{12} - 2\frac{8}{12}\). You need to regroup because \(\frac{3}{12}\) is less than \(\frac{8}{12}\). Borrow 1 from 4, which is \(\frac{12}{12}\). The problem becomes \(3\frac{3+12}{12} - 2\frac{8}{12} = 3\frac{15}{12} - 2\frac{8}{12} = 1\frac{7}{12}\) liters.

This is a two-step problem. First, subtract the amount poured out: \(10\frac{1}{2} - 3\frac{1}{3}\). The common denominator is 6. \(10\frac{3}{6} - 3\frac{2}{6} = 7\frac{1}{6}\) cups. Next, add the amount that was put back in: \(7\frac{1}{6} + 1\frac{1}{4}\). The common denominator is 12. \(7\frac{2}{12} + 1\frac{3}{12} = 8\frac{5}{12}\) cups.

First, find the time spent on math homework: \(2\frac{1}{2} - 1\frac{1}{3}\). The common denominator is 6. \(2\frac{3}{6} - 1\frac{2}{6} = 1\frac{1}{6}\) hours. Then, add the time spent on both tasks: \(2\frac{1}{2} + 1\frac{1}{6}\). The common denominator is 6. \(2\frac{3}{6} + 1\frac{1}{6} = 3\frac{4}{6}\), which simplifies to \(3\frac{2}{3}\) hours.

When you encounter a problem about combining parts to make a whole, you need to identify what information you have and what you're looking for. Here, you know the total distance and two of the three parts, so you need to find the missing third part.

To find the running distance, subtract the swimming and biking distances from the total distance: $$25\frac{1}{2} - 1\frac{1}{2} - 18\frac{3}{4}$$

First, subtract the swimming portion: $$25\frac{1}{2} - 1\frac{1}{2} = 24$$ miles remaining for biking and running.

Next, subtract the biking portion from what's left: $$24 - 18\frac{3}{4}$$. Convert 24 to a mixed number with fourths: $$24 = 23\frac{4}{4}$$. Now subtract: $$23\frac{4}{4} - 18\frac{3}{4} = 5\frac{1}{4}$$ miles for running.

Looking at the wrong answers: Choice A (24 miles) is what you get if you only subtract the swimming portion but forget about the biking. Choice B ($$6\frac{3}{4}$$ miles) likely results from an error in fraction subtraction, possibly adding fractions instead of subtracting. Choice C ($$20\frac{1}{4}$$ miles) is what you'd get if you only subtracted the swimming portion and made an arithmetic error.

The correct answer is D: $$5\frac{1}{4}$$ miles.

Study tip: In multi-step subtraction problems with mixed numbers, work systematically—subtract one portion at a time and double-check your fraction arithmetic. Convert whole numbers to equivalent fractions when needed to make subtraction easier.