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

1. What is $\frac{5}{8}+\frac{5}{8}$ written as a mixed number?

   $1\frac{2}{8}$. Add: $\frac{5+5}{8}=\frac{10}{8}=1\frac{2}{8}$ (convert improper to mixed).

2. What fraction more is $\frac{7}{9}$ than $\frac{4}{9}$?

   $\frac{3}{9}$. Find difference: $\frac{7}{9} - \frac{4}{9} = \frac{3}{9}$.

3. What is $\frac{8}{11} - \frac{3}{11}$?

   $\frac{5}{11}$. Subtract numerators: $8 - 3 = 5$, keep denominator $11$.

4. What is $\frac{4}{6}+\frac{1}{6}$ in simplest form?

   $\frac{5}{6}$. Add numerators: $4+1=5$; $\frac{5}{6}$ is already in simplest form.

5. Which equation matches: "Had $\frac{6}{9}$ L of juice, drank $\frac{2}{9}$ L; how much left"?

   $\frac{6}{9}-\frac{2}{9}=\frac{4}{9}$. Subtraction equation shows removing part from the original amount.

6. What is the missing number $x$ in $\frac{x}{7} + \frac{2}{7} = \frac{6}{7}$?

   $x = 4$. Since $4 + 2 = 6$, $x = 4$.

7. What fraction of a ribbon is used if you cut $\frac{5}{12}$ and then $\frac{4}{12}$ from the same ribbon?

   $\frac{9}{12}$. Add cut pieces: $\frac{5}{12} + \frac{4}{12} = \frac{9}{12}$.

8. What is $\frac{9}{9}-\frac{2}{9}$?

   $\frac{7}{9}$. Subtract numerators: $9-2=7$; keep denominator $9$.

9. What is $\frac{6}{12}+\frac{5}{12}$ in simplest form?

   $\frac{11}{12}$. Add numerators: $6+5=11$; $\frac{11}{12}$ is already in simplest form.

10. What operation should you use to find the total of $\frac{3}{8}$ of a pizza and $\frac{2}{8}$ of the same pizza?

    Add: $\frac{3}{8} + \frac{2}{8}$. Addition combines parts of the same whole.

11. What is the rule for subtracting fractions with like denominators, such as $\frac{a}{b} - \frac{c}{b}$?

    $\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$. Subtract numerators and keep the same denominator.

12. What is $1\frac{2}{9}+\frac{4}{9}$?

    $1\frac{6}{9}$. Add whole part to fraction: $1+\frac{2+4}{9}=1\frac{6}{9}$.

13. What is $1-\frac{3}{7}$?

    $\frac{4}{7}$. Rewrite $1$ as $\frac{7}{7}$, then subtract: $\frac{7}{7}-\frac{3}{7}=\frac{4}{7}$.

14. Which equation matches: "Ate $\frac{2}{8}$ of a pizza, then $\frac{3}{8}$ more; how much total"?

    $\frac{2}{8}+\frac{3}{8}=\frac{5}{8}$. Addition equation shows combining two parts of the same pizza.

15. Identify the correct equation for: A ribbon is $\frac{9}{10}$ yd long. You cut off $\frac{3}{10}$ yd. Length left?

    $\frac{9}{10} - \frac{3}{10} = \frac{6}{10}$. Subtract the cut length from the original length.

16. What fraction is shaded if a bar is split into $8$ equal parts and $5$ parts are shaded?

    $\frac{5}{8}$. Shaded parts over total parts gives the fraction.

17. What is the missing fraction in $\frac{2}{5} + \Box = \frac{4}{5}$?

    $\frac{2}{5}$. Since $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$.

18. What is $\frac{9}{12} - \frac{4}{12}$?

    $\frac{5}{12}$. Subtract numerators: $9 - 4 = 5$, keep denominator $12$.

19. What is the remaining ribbon if you have $\frac{9}{16}$ m and use $\frac{5}{16}$ m?

    $\frac{4}{16}$ m. Subtract used ribbon from total: $\frac{9-5}{16}=\frac{4}{16}$.

20. Identify the correct total: $\frac{1}{4}$ of a pan plus $\frac{2}{4}$ of the same pan equals what?

    $\frac{3}{4}$. Add parts of the same pan: $\frac{1+2}{4}=\frac{3}{4}$.

21. What is $\frac{5}{12} + \frac{4}{12}$?

    $\frac{9}{12}$. Add numerators: $5 + 4 = 9$, keep denominator $12$.

22. What is the total distance if you walk $\frac{7}{9}$ mile and $\frac{1}{9}$ mile?

    $\frac{8}{9}$ mile. Add distances with same denominator: $\frac{7+1}{9}=\frac{8}{9}$.

23. Find the missing fraction: $\frac{11}{15} - \frac{?}{15} = \frac{6}{15}$.

    $\frac{5}{15}$. Solve: $11 - ? = 6$, so $? = 5$.

24. What fraction of a pizza is left if you eat $\frac{3}{8}$ and then $\frac{2}{8}$ of the same pizza?

    $\frac{3}{8}$. Subtract eaten parts: $1 - \frac{3}{8} - \frac{2}{8} = \frac{3}{8}$.

25. Identify the correct difference: $\frac{5}{6}$ of a tank minus $\frac{1}{6}$ of the same tank equals what?

    $\frac{4}{6}$. Subtract parts of the same tank: $\frac{5-1}{6}=\frac{4}{6}$.

26. Find and correct the error: $\frac{9}{10} - \frac{2}{10} = \frac{7}{20}$.

    Correct: $\frac{9}{10} - \frac{2}{10} = \frac{7}{10}$. Error: denominator changed; keep it as $10$.

27. What is the missing number $x$ in $\frac{9}{13} - \frac{x}{13} = \frac{5}{13}$?

    $x = 4$. Since $9 - 4 = 5$, $x = 4$.

28. Identify the correct equation for: left after using $\frac{a}{b}$ then $\frac{c}{b}$ of one whole.

    $1 - \left(\frac{a}{b} + \frac{c}{b}\right)$. Subtract total used from whole.

29. What is the total time if you read $\frac{2}{6}$ hour and then $\frac{3}{6}$ hour?

    $\frac{5}{6}$ hour. Add time periods with same denominator: $\frac{2+3}{6}=\frac{5}{6}$.

30. Identify the correct equation for: You drank $\frac{2}{5}$ L, then $\frac{1}{5}$ L more. Total drank?

    $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$. Add the amounts drunk to find total consumption.

31. What is the difference $\frac{7}{10}-\frac{4}{10}$?

    $\frac{3}{10}$. Subtract numerators when denominators are the same: $7-4=3$.

32. What fraction of a whole is left after using $\frac{5}{12}$ and $\frac{3}{12}$ of it?

    $\frac{4}{12}$. Subtract used parts from whole: $\frac{12}{12}-\frac{5}{12}-\frac{3}{12}=\frac{4}{12}$.

33. What is $\frac{6}{9} + \frac{1}{9}$?

    $\frac{7}{9}$. Add numerators: $6 + 1 = 7$, keep denominator $9$.

34. What fraction of a meter is the total of $\frac{4}{10}$ m and $\frac{3}{10}$ m?

    $\frac{7}{10}$ m. Add numerators: $4 + 3 = 7$, keep denominator $10$.

35. What is the sum of $\frac{3}{8}$ and $\frac{2}{8}$?

    $\frac{5}{8}$. Add numerators when denominators are the same: $3+2=5$.

36. What is left of one whole after using $\frac{1}{6}$ and $\frac{2}{6}$ of the same whole?

    $\frac{3}{6}$. Calculate: $1 - \frac{1}{6} - \frac{2}{6} = \frac{3}{6}$.

37. What is $\frac{5}{8} - \frac{2}{8}$ as shown by a bar model split into $8$ equal parts?

    $\frac{3}{8}$. Remove $2$ shaded parts from $5$ shaded parts.

38. What is the rule for adding fractions with the same denominator $b$: ${a}{b} + {c}{b}$?

    $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$. Add numerators and keep the same denominator.

39. What total distance is walked if you walk $\frac{2}{6}$ mile and then $\frac{3}{6}$ mile?

    $\frac{5}{6}$ mile. Add distances: $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$.

40. What is $\frac{11}{16} - \frac{5}{16}$?

    $\frac{6}{16}$. Subtract numerators: $11 - 5 = 6$, keep denominator $16$.

41. What is $2\frac{1}{5}-\frac{3}{5}$?

    $1\frac{3}{5}$. Subtract fractions: $2\frac{1}{5}-\frac{3}{5}=1\frac{6}{5}-\frac{3}{5}=1\frac{3}{5}$.

42. Find the missing fraction: $\frac{4}{12} + \frac{?}{12} = \frac{9}{12}$.

    $\frac{5}{12}$. Solve: $4 + ? = 9$, so $? = 5$.

43. What operation should you use to find how much is left after eating $\frac{5}{10}$ from $\frac{9}{10}$ of the same whole?

    Subtract: $\frac{9}{10} - \frac{5}{10}$. Subtraction finds the difference between parts.

44. What distance remains if you walk $\frac{5}{9}$ mi of a $\frac{8}{9}$ mi route?

    $\frac{3}{9}$ mi. Subtract numerators: $8 - 5 = 3$, keep denominator $9$.

45. Find and correct the error: $\frac{3}{8} + \frac{4}{8} = \frac{7}{16}$.

    Correct: $\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$. Error: denominator changed; keep it as $8$.

46. What is the total time if you read for $\frac{2}{6}$ hour and then $\frac{3}{6}$ hour?

    $\frac{5}{6}$ hour. Add numerators: $2 + 3 = 5$, keep denominator $6$.

47. Which statement is true for like denominators: $\frac{a}{b} + \frac{c}{b}$ keeps the denominator $b$ or adds denominators?

    It keeps the denominator: $\frac{a+c}{b}$. Like denominators stay the same when adding.

48. What is $\frac{9}{9} - \frac{4}{9}$?

    $\frac{5}{9}$. Subtract: $9 - 4 = 5$, keep denominator $9$.

49. What is $\frac{6}{12} - \frac{3}{12}$ written in simplest form?

    $\frac{1}{4}$. Subtract: $6 - 3 = 3$, then simplify $\frac{3}{12} = \frac{1}{4}$.

50. What is $\frac{3}{8} + \frac{2}{8}$?

    $\frac{5}{8}$. Add numerators: $3 + 2 = 5$, keep denominator $8$.

51. What is $\frac{8}{11}-\frac{3}{11}$?

    $\frac{5}{11}$. Subtract numerators: $8-3=5$; keep denominator $11$.

52. What is the rule for adding fractions with like denominators, such as $\frac{a}{b} + \frac{c}{b}$?

    $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$. Add numerators and keep the same denominator.

53. What is the rule for subtracting fractions with the same denominator $b$: $\frac{a}{b} - \frac{c}{b}$?

    $\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$. Subtract numerators and keep the same denominator.

54. What is the missing subtrahend in $\frac{11}{12}-\square=\frac{5}{12}$?

    $\frac{6}{12}$. Find what subtracts from $\frac{11}{12}$ to get $\frac{5}{12}$: $11-5=6$.

55. What fraction of a tank remains if it was $\frac{7}{10}$ full and you used $\frac{4}{10}$ of a tank?

    $\frac{3}{10}$. Subtract used from full: $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$.

56. What is $\frac{3}{7} + \frac{2}{7}$?

    $\frac{5}{7}$. Add numerators: $3 + 2 = 5$, keep denominator $7$.

57. What is the missing addend in $\frac{3}{10}+\square=\frac{9}{10}$?

    $\frac{6}{10}$. Find what adds to $\frac{3}{10}$ to get $\frac{9}{10}$: $9-3=6$.

58. What is $\frac{7}{10} - \frac{3}{10}$?

    $\frac{4}{10}$. Subtract numerators: $7 - 3 = 4$, keep denominator $10$.

59. What fraction of a gallon is left if a jug has $\frac{7}{8}$ gal and you pour out $\frac{1}{8}$ gal?

    $\frac{6}{8}$ gal. Subtract numerators: $7 - 1 = 6$, keep denominator $8$.

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