Add and Subtract Mixed Numbers - 4th Grade Math

1. What is $4\frac{3}{10}+0\frac{7}{10}$ in simplest form?

   $5$. $4+0=4$, $\frac{3}{10}+\frac{7}{10}=\frac{10}{10}=1$; total is $5$.

2. What is $6\ \frac{3}{10}+1\ \frac{9}{10}$ in simplest mixed-number form?

   $8\ \frac{2}{10}$. $6+1=7$ and $\frac{3}{10}+\frac{9}{10}=\frac{12}{10}=1\frac{2}{10}$, so $7+1\frac{2}{10}=8\frac{2}{10}$.

3. What is the renamed form of $3\frac{2}{5}$ after borrowing $1$ whole?

   $2\frac{7}{5}$. Borrow $1=\frac{5}{5}$: $3\frac{2}{5}=2+\frac{5}{5}+\frac{2}{5}=2\frac{7}{5}$.

4. What is $4\ \frac{5}{8}+2\ \frac{6}{8}$ in simplest mixed-number form?

   $7\ \frac{3}{8}$. $4+2=6$ and $\frac{5}{8}+\frac{6}{8}=\frac{11}{8}=1\frac{3}{8}$, so $6+1\frac{3}{8}=7\frac{3}{8}$.

5. What should you do if you need to subtract and the top fraction is smaller, like $5\ \frac{1}{6}-2\ \frac{5}{6}$?

   Regroup: borrow $1$ from the whole number and add it to the fraction. This converts the whole number to allow subtraction when top fraction is smaller.

6. What is $5\ \frac{5}{6}-2\ \frac{1}{6}$?

   $3\ \frac{4}{6}$. $5-2=3$ and $\frac{5}{6}-\frac{1}{6}=\frac{4}{6}$.

7. What is $2\frac{5}{6}+3\frac{4}{6}$ in simplest form?

   $6\frac{1}{2}$. $2+3=5$, $\frac{5}{6}+\frac{4}{6}=\frac{9}{6}=1\frac{3}{6}=1\frac{1}{2}$.

8. What is $8 \frac{1}{6}+2 \frac{5}{6}$ in simplest mixed-number form?

   $11$. $8+2=10$ and $\frac{1}{6}+\frac{5}{6}=\frac{6}{6}=1$, so $10+1=11$.

9. What is $4\ \frac{3}{7}+1\ \frac{6}{7}$?

   $6\ \frac{2}{7}$. $4+1=5$ and $\frac{3}{7}+\frac{6}{7}=\frac{9}{7}=1\frac{2}{7}$, so $5+1\frac{2}{7}=6\frac{2}{7}$.

10. What is $2\ \frac{4}{7}+3\ \frac{2}{7}$?

    $5\ \frac{6}{7}$. $2+3=5$ and $\frac{4}{7}+\frac{2}{7}=\frac{6}{7}$.

11. What is $5-2\ \frac{3}{6}$ in simplest mixed-number form?

    $2\ \frac{3}{6}$. $5=4\frac{6}{6}$, then $4\frac{6}{6}-2\frac{3}{6}=2\frac{3}{6}$.

12. What is $3 \frac{2}{7} + 4 \frac{1}{7}$?

    $7 \frac{3}{7}$. $3+4=7$ and $\frac{2}{7}+\frac{1}{7}=\frac{3}{7}$.

13. What is the first step to add mixed numbers with like denominators?

    Add whole numbers and add fractional parts with the same denominator. This separates the whole and fractional parts for easier calculation.

14. What is $7\ \frac{6}{9}+2\ \frac{1}{9}$?

    $9\ \frac{7}{9}$. $7+2=9$ and $\frac{6}{9}+\frac{1}{9}=\frac{7}{9}$.

15. What is $1\ \frac{7}{12}+2\ \frac{8}{12}$ in simplest mixed-number form?

    $4\ \frac{3}{12}$. $1+2=3$ and $\frac{7}{12}+\frac{8}{12}=\frac{15}{12}=1\frac{3}{12}$, so $3+1\frac{3}{12}=4\frac{3}{12}$.

16. What is $3\ \frac{2}{5}+1\ \frac{1}{5}$?

    $4\ \frac{3}{5}$. $3+1=4$ and $\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$.

17. What is the renamed form of $5\frac{1}{8}$ after borrowing $1$ whole?

    $4\frac{9}{8}$. Borrow $1=\frac{8}{8}$: $5\frac{1}{8}=4+\frac{8}{8}+\frac{1}{8}=4\frac{9}{8}$.

18. What is $2\frac{1}{3}+2\frac{2}{3}$ in simplest form?

    $5$. $2+2=4$, $\frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1$; total is $5$.

19. What is $7\ \frac{1}{4}-3\ \frac{3}{4}$ in simplest mixed-number form?

    $3\ \frac{2}{4}$. Borrow: $7\frac{1}{4}=6\frac{5}{4}$, then $6-3=3$ and $\frac{5}{4}-\frac{3}{4}=\frac{2}{4}$.

20. What is $\frac{27}{5}$ written as a mixed number in simplest form?

    $5\frac{2}{5}$. Divide: $27÷5=5$ remainder $2$.

21. What is $6\ \frac{1}{4}-2\ \frac{3}{4}$?

    $3\ \frac{2}{4}$. Regroup: $6\frac{1}{4}=5\frac{5}{4}$, then $5-2=3$ and $\frac{5}{4}-\frac{3}{4}=\frac{2}{4}$.

22. What is $5\ \frac{6}{9}-2\ \frac{4}{9}$?

    $3\ \frac{2}{9}$. $5-2=3$ and $\frac{6}{9}-\frac{4}{9}=\frac{2}{9}$.

23. What is $9\ \frac{2}{5}-4\ \frac{4}{5}$?

    $4\ \frac{3}{5}$. Regroup: $9\frac{2}{5}=8\frac{7}{5}$, then $8-4=4$ and $\frac{7}{5}-\frac{4}{5}=\frac{3}{5}$.

24. What is $1\frac{7}{12}+2\frac{8}{12}$ in simplest form?

    $4\frac{1}{4}$. $1+2=3$, $\frac{7}{12}+\frac{8}{12}=\frac{15}{12}=1\frac{3}{12}=1\frac{1}{4}$.

25. What improper fraction equals the mixed number $3 \frac{2}{7}$?

    $\frac{23}{7}$. Multiply whole number by denominator and add numerator: $3×7+2=23$.

26. What is $6\frac{3}{10}+2\frac{9}{10}$ in simplest form?

    $9\frac{1}{5}$. $6+2=8$, $\frac{3}{10}+\frac{9}{10}=\frac{12}{10}=1\frac{2}{10}=1\frac{1}{5}$.

27. What is the first step to add mixed numbers with like denominators?

    Add the whole numbers and add the fractional parts. This separates the problem into simpler parts to solve.

28. What is $8\ \frac{1}{5}+2\ \frac{4}{5}$?

    $11$. $8+2=10$ and $\frac{1}{5}+\frac{4}{5}=\frac{5}{5}=1$, so $10+1=11$.

29. What is $12 \frac{3}{10} - 5 \frac{9}{10}$?

    $6 \frac{4}{10}$. Regroup: $12\frac{3}{10}=11\frac{13}{10}$, then $11-5=6$ and $\frac{13}{10}-\frac{9}{10}=\frac{4}{10}$.

30. What is $10\ \frac{7}{8}-3\ \frac{2}{8}$?

    $7\ \frac{5}{8}$. $10-3=7$ and $\frac{7}{8}-\frac{2}{8}=\frac{5}{8}$.

31. What is $3\frac{1}{6}+2\frac{4}{6}$ in simplest form?

    $5\frac{5}{6}$. $3+2=5$, $\frac{1}{6}+\frac{4}{6}=\frac{5}{6}$.

32. What is the first step to subtract mixed numbers with like denominators when the top fraction is large enough?

    Subtract whole numbers and subtract fractional parts. This works when the first fraction is larger than the second.

33. What is $3\ \frac{5}{9}-\frac{2}{9}$?

    $3\ \frac{3}{9}$. $\frac{5}{9}-\frac{2}{9}=\frac{3}{9}$, whole number stays $3$.

34. Identify the missing number: $8\ \frac{5}{6}-\Box=3\ \frac{1}{6}$.

    $5\ \frac{4}{6}$. $8\frac{5}{6}-3\frac{1}{6}=5\frac{4}{6}$.

35. What is $1\ \frac{7}{10}+3\ \frac{4}{10}$?

    $5\ \frac{1}{10}$. $1+3=4$ and $\frac{7}{10}+\frac{4}{10}=\frac{11}{10}=1\frac{1}{10}$, so $4+1\frac{1}{10}=5\frac{1}{10}$.

36. What is $6\ \frac{5}{8}+2\ \frac{3}{8}$?

    $9$. $6+2=8$ and $\frac{5}{8}+\frac{3}{8}=\frac{8}{8}=1$, so $8+1=9$.

37. What is the rule for subtracting mixed numbers with like denominators?

    Subtract whole parts and fractional parts; rename by borrowing $1$ if needed. Borrow from whole number when fraction is too small.

38. What is $9\frac{2}{7}-4\frac{6}{7}$ in simplest form?

    $4\frac{3}{7}$. Rename $9\frac{2}{7}$ as $8\frac{9}{7}$; $8-4=4$, $\frac{9}{7}-\frac{6}{7}=\frac{3}{7}$.

39. What is $8\frac{1}{6}-3\frac{5}{6}$ in simplest form?

    $4\frac{1}{3}$. Rename $8\frac{1}{6}$ as $7\frac{7}{6}$; $7-3=4$, $\frac{7}{6}-\frac{5}{6}=\frac{2}{6}=\frac{1}{3}$.

40. What is the first step to subtract mixed numbers with like denominators?

    Subtract whole numbers and subtract fractional parts with the same denominator. This separates the whole and fractional parts for easier calculation.

41. What is $2 \frac{3}{8} + \frac{4}{8}$ in simplest mixed-number form?

    $2 \frac{7}{8}$. $\frac{3}{8}+\frac{4}{8}=\frac{7}{8}$, so result is $2 \frac{7}{8}$.

42. What is $10\ \frac{1}{8}-6\ \frac{7}{8}$ in simplest mixed-number form?

    $3\ \frac{2}{8}$. Borrow: $10\frac{1}{8}=9\frac{9}{8}$, then $9-6=3$ and $\frac{9}{8}-\frac{7}{8}=\frac{2}{8}$.

43. What is $2\frac{3}{8}$ written as an improper fraction?

    $\frac{19}{8}$. Multiply whole by denominator, add numerator: $2 \times 8 + 3 = 19$.

44. What is $9\ \frac{2}{5}-4\ \frac{4}{5}$ in simplest mixed-number form?

    $4\ \frac{3}{5}$. Borrow: $9\frac{2}{5}=8\frac{7}{5}$, then $8-4=4$ and $\frac{7}{5}-\frac{4}{5}=\frac{3}{5}$.

45. What is $7\frac{2}{5}-3\frac{1}{5}$ in simplest form?

    $4\frac{1}{5}$. $7-3=4$, $\frac{2}{5}-\frac{1}{5}=\frac{1}{5}$.

46. Identify the missing number: $2\ \frac{3}{8}+\Box=5\ \frac{7}{8}$.

    $3\ \frac{4}{8}$. $5\frac{7}{8}-2\frac{3}{8}=3\frac{4}{8}$.

47. What mixed number equals the improper fraction $\frac{17}{4}$?

    $4\ \frac{1}{4}$. Divide: $17÷4=4$ remainder $1$, so $\frac{17}{4}=4\frac{1}{4}$.

48. What is $5\frac{1}{4}-2\frac{3}{4}$ in simplest form?

    $2\frac{1}{2}$. Rename $5\frac{1}{4}$ as $4\frac{5}{4}$; $4-2=2$, $\frac{5}{4}-\frac{3}{4}=\frac{2}{4}=\frac{1}{2}$.

49. What is the rule for adding mixed numbers with like denominators?

    Add whole parts; add fractional parts with the same denominator; regroup if needed. Add separately, then combine and simplify.

50. What is $4\frac{5}{9}+1\frac{7}{9}$ in simplest form?

    $6\frac{1}{3}$. $4+1=5$, $\frac{5}{9}+\frac{7}{9}=\frac{12}{9}=1\frac{3}{9}=1\frac{1}{3}$.

51. What is $\left(3\ \frac{1}{9}+2\ \frac{8}{9}\right)-1\ \frac{4}{9}$?

    $4\ \frac{5}{9}$. First add: $3\frac{1}{9}+2\frac{8}{9}=5\frac{9}{9}=6$, then $6-1\frac{4}{9}=4\frac{5}{9}$.

52. What is $12\ \frac{3}{6}-5\ \frac{5}{6}$ in simplest mixed-number form?

    $6\ \frac{4}{6}$. Borrow: $12\frac{3}{6}=11\frac{9}{6}$, then $11-5=6$ and $\frac{9}{6}-\frac{5}{6}=\frac{4}{6}$.

53. What is $10\frac{3}{4}-6\frac{1}{4}$ in simplest form?

    $4\frac{1}{2}$. $10-6=4$, $\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$.

54. What is $7\frac{5}{6}-7\frac{2}{6}$ in simplest form?

    $\frac{1}{2}$. $7-7=0$, $\frac{5}{6}-\frac{2}{6}=\frac{3}{6}=\frac{1}{2}$.

55. What is $6\frac{5}{8}-1\frac{7}{8}$ in simplest form?

    $4\frac{3}{4}$. Rename $6\frac{5}{8}$ as $5\frac{13}{8}$; $5-1=4$, $\frac{13}{8}-\frac{7}{8}=\frac{6}{8}=\frac{3}{4}$.

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