Solve Fraction Addition/Subtraction Word Problems - 4th Grade Math

Maya ate $\frac{2}{8}$ of a pizza for lunch and $\frac{3}{8}$ of the same pizza for dinner. She then gave $\frac{1}{8}$ of the pizza to her brother. What fraction of the original pizza does Maya have left?
Answer: $\frac{2}{8}$ Maya ate and gave away 2/8 plus 3/8 plus 1/8, which totals 6/8 of the pizza, so subtracting that from the whole pizza gives 8/8 minus 6/8 equals 2/8, making Choice D correct. Choice A, 6/8, is the total amount eaten and given away, not what remains. Choice B, 4/8, comes from combining only two of the three amounts instead of all three. Choice C, 5/8, comes from a small addition error when combining the three fractions.
Chen had $\tfrac{7}{10}$ of a pie left. He ate $\tfrac{3}{10}$ of the same pie. What fraction of the pie is left?
Answer: $\tfrac{4}{10}$ of the pie The correct answer is 4/10, because 7/10 minus 3/10 equals 4/10 when subtracting the numerators and keeping the same denominator. Choice A, 10/10, wrongly adds the numerators instead of subtracting. Choice B, 10/20, mistakenly adds both the numerators and the denominators. Choice C, 3/10, just repeats the amount Chen ate instead of finding what is left.
A recipe calls for $\frac{3}{6}$ cup of flour for the base and $\frac{2}{6}$ cup of flour for the topping. Jake accidentally used $\frac{4}{6}$ cup of flour total. What should Jake do to correct the amount of flour?
Answer: $\frac{1}{6}$ cup of flour needs to be added Jake needs 5/6 cup total (3/6 + 2/6) but used only 4/6 cup, so he needs to add 1/6 cup more. Choice A incorrectly suggests removing flour when more is actually needed. Choice B is short of the full amount still needed. Choice C represents the whole recipe amount, not the amount still missing.
Luis had $\frac{8}{10}$ of a chocolate bar. He ate $\frac{3}{10}$ of the bar and gave $\frac{2}{10}$ to his sister. Later, his mom gave him $\frac{4}{10}$ of another identical chocolate bar. How much chocolate does Luis have now compared to one whole bar?
Answer: Luis now has $\frac{7}{10}$ of a chocolate bar When you see a fraction word problem with multiple steps, you need to carefully track what happens to the amount at each step, just like following money in and out of a piggy bank. Let's follow Luis's chocolate step by step. He starts with $\frac{8}{10}$ of a bar. Then he loses some: he eats $\frac{3}{10}$ and gives away $\frac{2}{10}$ . Since all fractions have the same denominator (10), you can subtract directly: $\frac{8}{10} - \frac{3}{10} - \frac{2}{10} = \frac{3}{10}$ . Now Luis has $\frac{3}{10}$ left from his original bar. But then his mom gives him $\frac{4}{10}$ of another identical bar. Since you're adding chocolate, you add the fractions: $\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$ . So Luis ends up with $\frac{7}{10}$ of a chocolate bar. Looking at the wrong answers: Choice A ( $\frac{9}{10}$ ) likely comes from forgetting to subtract what Luis ate - maybe only subtracting the $\frac{2}{10}$ he gave away. Choice B ( $\frac{3}{10}$ ) stops too early, showing only what Luis had after eating and sharing but before getting more from his mom. Choice D ( $\frac{17}{10}$ ) adds all the numbers together (8 + 3 + 2 + 4 = 17) without paying attention to whether amounts are being added or subtracted. Remember: when solving multi-step fraction problems, work through each action one at a time and pay careful attention to whether each step increases or decreases the total amount.
Maya ate $\tfrac{2}{8}$ of a pizza. Jamal ate $\tfrac{3}{8}$ of the same pizza. What fraction of the pizza did they eat altogether?
Answer: $\tfrac{5}{8}$ of the pizza Adding the two fractions of pizza eaten gives 2/8 + 3/8 = 5/8 of the pizza. Choice A incorrectly adds the denominators together as well as the numerators. Choice C is only Maya's portion, not their combined total. Choice D reflects a small error in adding the numerators.
A water tank was $\frac{5}{8}$ full at the start of the day. During the morning, $\frac{2}{8}$ of the tank's capacity was used. In the afternoon, $\frac{3}{8}$ of the tank's capacity was added back. What fraction of the tank is full at the end of the day?
Answer: The tank is $\frac{6}{8}$ full at day's end Starting with $\frac{5}{8}$ , after using $\frac{2}{8}$ : $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$ . After adding $\frac{3}{8}$ : $\frac{3}{8} + \frac{3}{8} = \frac{6}{8}$ . Choice B represents the amount after morning use but before afternoon addition. Choice C incorrectly adds all three fractions. Choice D would mean the tank is empty.
A container was $10/12$ full of water. After some water was used, it was $7/12$ full. How much water was used?
Answer: $3/12$ of the container Choice B is correct because 10/12 minus 7/12 equals 3/12 of the container. Choice A is incorrect because it results from adding instead of subtracting the two amounts. Choice C is incorrect because it repeats the starting amount instead of finding the difference. Choice D is incorrect because it changes the denominator in a way that does not match twelfths.
A container was filled with $\tfrac{5}{6}$ of a tank of water. Marcus used $\tfrac{2}{6}$ of the water from that same container. How much water is left in the container?
Answer: $\tfrac{3}{6}$ of the container Since the container started with 5/6 of a tank and Marcus used 2/6, subtracting gives 5/6 minus 2/6 equals 3/6, making Choice A correct. Choice B, 5/12 of the container, comes from multiplying the denominators instead of subtracting the fractions directly. Choice C, 7/6 of the container, comes from adding the two fractions instead of subtracting them. Choice D, 2/6 of the container, is simply the amount Marcus used, not the amount remaining.
A hiking trail is 1 mile long. Marcus walked 5/8 of the same mile. How much of the mile does he still have left to walk?
Answer: 3/8 mile The whole trail is 8/8, so subtracting the 5/8 Marcus already walked leaves 3/8 of a mile. Choice D (5/8) is the distance already walked, not what remains. Choice C (2/8) comes from a subtraction slip. Choice A (3/16) results from incorrectly changing the denominator.
Carlos painted $\tfrac{6}{10}$ of a poster. Later, he painted $\tfrac{2}{10}$ more of the same poster. What fraction of the poster is painted in all?
Answer: $\tfrac{8}{10}$ of the poster The correct answer is D, 8/10 of the poster. Adding the two amounts painted gives 6/10 + 2/10 = 8/10. Choice A, 6/10, restates only the first amount painted rather than the total. Choice B, 4/10, comes from subtracting instead of adding. Choice C, 8/20, comes from also adding the denominators together instead of keeping them the same.
A hiking path is 9/12 mile long. Amir has walked 4/12 mile on the same path. What fraction of a mile does Amir have left to walk?
Answer: 5/12 mile Since both fractions refer to the same path and share the denominator 12, subtract: 9 - 4 = 5, giving 5/12 mile remaining. Choice A (4/12) is the distance already walked, not what's left. Choice B (13/12) comes from adding instead of subtracting. Choice C (9/24) results from incorrectly changing the denominator.
Sofia walked $4/6$ of a mile. Amir walked $1/6$ of the same mile. How much farther did Sofia walk than Amir?
Answer: $3/6$ mile Sofia walked 4/6 of a mile and Amir walked 1/6 of the same mile, so the difference is 4/6 minus 1/6, which is 3/6 mile, making Choice A correct. Choice B, 5/6 mile, comes from adding the two distances together instead of subtracting them. Choice C, 3/12 mile, comes from subtracting the denominators as well as the numerators, instead of keeping the denominator the same. Choice D, 4/6 mile, is simply Sofia's distance alone, without subtracting Amir's distance at all. Subtracting the numerators while keeping the same denominator gives how much farther Sofia walked.
Refer to the diagram. Sarah shaded $\frac{2}{5}$ of the rectangle on Monday and $\frac{1}{5}$ more on Tuesday. On Wednesday, she erased the shading from $\frac{2}{5}$ of the rectangle. What fraction of the rectangle is shaded now?
Answer: $\frac{1}{5}$ of the rectangle remains shaded Sarah shaded $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$ by Tuesday. On Wednesday she erased $\frac{2}{5}$ , leaving $\frac{3}{5} - \frac{2}{5} = \frac{1}{5}$ shaded. Choice B represents how much was shaded before Wednesday's erasing. Choice C represents either Monday's amount or Wednesday's erased amount. Choice D would mean the entire rectangle is shaded.
Maya ate $\frac{2}{8}$ of a pizza. Jamal ate $\frac{3}{8}$ of the same pizza. What fraction of the pizza did they eat altogether?
Answer: $\frac{5}{8}$ of the pizza $\frac{5}{8}$ is correct because $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$ . $\frac{5}{16}$ is incorrect because it results from multiplying the denominators instead of keeping a common denominator. $\frac{7}{8}$ is incorrect because it does not match the sum of the numerators. $\frac{4}{8}$ is incorrect because it drops the numerator of one fraction instead of adding both.
A container was $\tfrac{5}{12}$ full of water. Marcus used $\tfrac{2}{12}$ of the same container. How much water is left in the container?
Answer: $\tfrac{3}{12}$ of the container Choice B is correct because 5/12 minus 2/12 equals 3/12 of the container. Choice A is incorrect because it does not match the correct difference. Choice C is incorrect because it adds the two fractions instead of subtracting. Choice D is incorrect because it changes the denominator in a way that does not match twelfths.
Emma walked 4/7 of the way to school when she realized she forgot her backpack. She turned around and walked the same 4/7 of the way back home, then walked 6/7 of the way to school again before her mom picked her up. What fraction of the distance to school did Emma walk in all?
Answer: 14/7 of the distance to school Emma walked 4/7 to get partway to school, then 4/7 back home (the same distance), then 6/7 toward school again, for a total of 4/7 + 4/7 + 6/7 = 14/7. Choice A (10/7) leaves out one of the 4/7 legs of the trip. Choices C (6/7) and D (4/7) only account for one part of Emma's total walk.
Chen had $\tfrac{7}{10}$ of a pie left on a plate. He ate $\tfrac{3}{10}$ of that same pie. What fraction of the pie is remaining?
Answer: $\tfrac{4}{10}$ of the pie The correct answer is C, 4/10 of the pie. Subtracting the amount eaten from the amount Chen had gives 7/10 minus 3/10 equals 4/10. Choice A, 10/10, comes from adding instead of subtracting. Choice B, 3/10, simply restates the amount eaten instead of finding what is left. Choice D, 7/30, comes from also subtracting the denominators instead of keeping them the same.
Sofia walked $\tfrac{4}{5}$ mile on a trail. Amir walked $\tfrac{2}{5}$ mile on the same trail. How much farther did Sofia walk than Amir?
Answer: $\tfrac{2}{5}$ mile Choice B is correct because 4/5 minus 2/5 equals 2/5 mile. Choice A is incorrect because it results from adding instead of subtracting the two distances. Choice C is incorrect because it simply repeats Sofia's distance instead of finding the difference. Choice D is incorrect because it changes the denominator in a way that does not match fifths.
Yuki used $\tfrac{2}{10}$ of a roll of tape for a project. Then she used $\tfrac{5}{10}$ more from the same roll. What fraction of the roll did she use in all?
Answer: $\tfrac{7}{10}$ of the roll Choice B is correct because 2/10 plus 5/10 equals 7/10 of the roll. Choice A is incorrect because it does not match the sum of the two amounts. Choice C is incorrect because it changes the denominator in a way that does not match tenths. Choice D is incorrect because it results from subtracting instead of adding.
Emma used $\tfrac{3}{12}$ of a yard of ribbon. Then she used $\tfrac{5}{12}$ more of the same yard of ribbon. What fraction of the yard did she use in all?
Answer: $\tfrac{8}{12}$ of a yard The correct answer is D, 8/12 of a yard. Adding the two amounts of ribbon means adding the numerators while keeping the same denominator: 3/12 + 5/12 = 8/12. Choices A and C come from also adding the denominators together instead of keeping them the same. Choice B comes from a simple counting error when combining the numerators.

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