Add and Subtract Unlike Fractions - 5th Grade Math

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

   $2\frac{7}{12}$. Convert to twelfths: $\frac{64}{12}-\frac{33}{12}=\frac{31}{12}=2\frac{7}{12}$.

2. What is $\frac{3}{5}+\frac{1}{2}$? Give the answer as a simplified fraction.

   $\frac{11}{10}$. Convert to $\frac{6}{10}+\frac{5}{10}=\frac{11}{10}$ using LCD 10.

3. What is $\frac{2}{3}+\frac{5}{4}$? Give the answer as an improper fraction in simplest form.

   $\frac{23}{12}$. Convert to $\frac{8}{12}+\frac{15}{12}$ using LCD 12.

4. What is $\frac{2}{3}+\frac{5}{4}$? Give the answer as a simplified improper fraction.

   $\frac{23}{12}$. Convert to $\frac{8}{12}+\frac{15}{12}=\frac{23}{12}$ using LCD 12.

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

   $1\frac{11}{12}$. Convert to twelfths: $\frac{33}{12}-\frac{10}{12}=\frac{23}{12}=1\frac{11}{12}$.

6. What is $\frac{11}{12}-\frac{5}{8}$? Give the answer in simplest form.

   $\frac{7}{24}$. Convert to $\frac{22}{24}-\frac{15}{24}$ using LCD 24.

7. What is $\frac{4}{7}+\frac{3}{14}$? Give the answer in simplest form.

   $\frac{11}{14}$. Convert to $\frac{8}{14}+\frac{3}{14}$ using LCD 14.

8. What is $3\frac{1}{5}-1\frac{1}{2}$? Give the answer as a simplified mixed number.

   $1\frac{7}{10}$. Convert to improper fractions, subtract using LCD 10.

9. What is $\frac{9}{10}-\frac{2}{5}$ in simplest form?

   $\frac{1}{2}$. Convert to tenths: $\frac{9}{10}-\frac{4}{10}=\frac{5}{10}=\frac{1}{2}$.

10. What is $\frac{5}{12}+\frac{1}{8}$? Give the answer in simplest form.

    $\frac{13}{24}$. Convert to $\frac{10}{24}+\frac{3}{24}$ using LCD 24.

11. What is the least common denominator (LCD) of $\frac{1}{9}$ and $\frac{1}{12}$?

    $36$. LCD is the smallest number divisible by both 9 and 12.

12. What is $\frac{9}{10}-\frac{2}{15}$? Give the answer in simplest form.

    $\frac{23}{30}$. Convert to $\frac{27}{30}-\frac{4}{30}$ using LCD 30.

13. Convert the improper fraction $\frac{17}{6}$ to a mixed number.

    $2\frac{5}{6}$. Divide 17 by 6: quotient 2, remainder 5.

14. What is the least common denominator (LCD) of $\frac{1}{6}$ and $\frac{1}{8}$?

    $24$. LCD is the smallest number divisible by both 6 and 8.

15. Identify the missing number: $\frac{3}{4}=\frac{?}{20}$.

    $15$. Multiply numerator and denominator by 5 to get equivalent fraction.

16. What is $\frac{11}{12}-\frac{5}{8}$? Give the answer as a simplified fraction.

    $\frac{7}{24}$. Convert to $\frac{22}{24}-\frac{15}{24}=\frac{7}{24}$ using LCD 24.

17. State the general formula for $\frac{a}{b}-\frac{c}{d}$ using a common denominator.

    $\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$. Cross-multiply and subtract numerators over the product of denominators.

18. What is $\frac{5}{6}-\frac{1}{4}$ in simplest form?

    $\frac{7}{12}$. Convert to twelfths: $\frac{10}{12}-\frac{3}{12}=\frac{7}{12}$.

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

    $\frac{11}{12}$. Convert to twelfths: $\frac{8}{12}+\frac{3}{12}=\frac{11}{12}$.

20. What is $\frac{3}{10}+\frac{1}{5}$ in simplest form?

    $\frac{1}{2}$. Convert to tenths: $\frac{3}{10}+\frac{2}{10}=\frac{5}{10}=\frac{1}{2}$.

21. Identify the equivalent fraction: $\frac{7}{8}=\frac{?}{32}$.

    $\frac{28}{32}$. Multiply numerator and denominator by 4 since $8×4=32$.

22. What is $\frac{3}{10}+\frac{7}{15}$? Give the answer in simplest form.

    $\frac{23}{30}$. Convert to $\frac{9}{30}+\frac{14}{30}$ using LCD 30.

23. What is $3\frac{1}{5}-\frac{3}{4}$? Give the answer as a mixed number in simplest form.

    $2\frac{9}{20}$. Convert to $\frac{16}{5}-\frac{3}{4}$ using LCD 20.

24. What is $1\frac{1}{2}+\frac{2}{3}$? Give the answer as a simplified mixed number.

    $2\frac{1}{6}$. Convert $1\frac{1}{2}$ to $\frac{3}{2}$, then add using LCD 6.

25. What is $1\frac{1}{2}+\frac{2}{3}$? Give the answer as a mixed number in simplest form.

    $2\frac{1}{6}$. Convert $1\frac{1}{2}$ to $\frac{3}{2}$, then add using LCD 6.

26. Find and correct the sum: $\frac{1}{2}+\frac{1}{3}=\frac{2}{5}$.

    Correct sum: $\frac{5}{6}$. Common denominator is 6: $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$, not $\frac{2}{5}$.

27. What is $\frac{7}{8}-\frac{1}{3}$? Give the answer in simplest form.

    $\frac{13}{24}$. Convert to $\frac{21}{24}-\frac{8}{24}$ using LCD 24.

28. What is $3\frac{1}{5}+1\frac{1}{2}$ in simplest form?

    $4\frac{7}{10}$. Convert to tenths: $\frac{32}{10}+\frac{15}{10}=\frac{47}{10}=4\frac{7}{10}$.

29. What is $\frac{7}{8}-\frac{1}{3}$? Give the answer as a simplified fraction.

    $\frac{13}{24}$. Convert to $\frac{21}{24}-\frac{8}{24}=\frac{13}{24}$ using LCD 24.

30. What is the least common denominator (LCD) of $\frac{1}{9}$ and $\frac{1}{12}$?

    $36$. Find the LCM of 9 and 12 by factoring: $9=3^2$, $12=2^2\times3$.

31. What is $\frac{3}{7}+\frac{2}{21}$? Give the answer as a simplified fraction.

    $\frac{11}{21}$. Convert to $\frac{9}{21}+\frac{2}{21}=\frac{11}{21}$ using LCD 21.

32. What is $\frac{5}{8}+\frac{3}{16}$ in simplest form?

    $\frac{13}{16}$. Convert to sixteenths: $\frac{10}{16}+\frac{3}{16}=\frac{13}{16}$.

33. Find and correct the difference: $\frac{3}{4}-\frac{1}{6}=\frac{2}{8}$.

    Correct difference: $\frac{7}{12}$. Common denominator is 12: $\frac{9}{12}-\frac{2}{12}=\frac{7}{12}$, not $\frac{2}{8}$.

34. What is $2\frac{1}{3}-\frac{3}{4}$? Give the answer as a simplified mixed number.

    $1\frac{7}{12}$. Convert $2\frac{1}{3}$ to $\frac{7}{3}$, subtract using LCD 12.

35. What is $\frac{7}{12}+\frac{5}{18}$? Give the answer as a simplified fraction.

    $\frac{31}{36}$. Convert to $\frac{21}{36}+\frac{10}{36}=\frac{31}{36}$ using LCD 36.

36. What is $\frac{5}{6}-\frac{1}{4}$? Give the answer as a simplified fraction.

    $\frac{7}{12}$. Convert to $\frac{10}{12}-\frac{3}{12}=\frac{7}{12}$ using LCD 12.

37. State the general formula for $\frac{a}{b}+\frac{c}{d}$ using a common denominator.

    $\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$. Cross-multiply to find common denominator $bd$, then add numerators.

38. What is $\frac{4}{9}+\frac{5}{6}$? Give the answer as a simplified fraction.

    $\frac{23}{18}$. Convert to $\frac{8}{18}+\frac{15}{18}=\frac{23}{18}$ using LCD 18.

39. What is $\frac{3}{5}+\frac{1}{2}$? Give the answer in simplest form.

    $\frac{11}{10}$. Convert to $\frac{6}{10}+\frac{5}{10}$ using LCD 10.

40. What is $\frac{4}{9}+\frac{1}{3}$ in simplest form?

    $\frac{7}{9}$. Convert to ninths: $\frac{4}{9}+\frac{3}{9}=\frac{7}{9}$.

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

    $2\frac{1}{6}$. Convert to sixths: $\frac{9}{6}+\frac{4}{6}=\frac{13}{6}=2\frac{1}{6}$.

42. Identify the missing number: $\frac{5}{6}=\frac{?}{24}$.

    $20$. Multiply numerator and denominator by 4 to get equivalent fraction.

43. What is $\frac{7}{12}-\frac{1}{6}$ in simplest form?

    $\frac{5}{12}$. Convert to twelfths: $\frac{7}{12}-\frac{2}{12}=\frac{5}{12}$.

44. What is $\frac{9}{10}+\frac{2}{15}$? Give the answer as a simplified fraction.

    $\frac{31}{30}$. Convert to $\frac{27}{30}+\frac{4}{30}=\frac{31}{30}$ using LCD 30.

45. Find and correct the error: $\frac{1}{2}+\frac{1}{3}=\frac{2}{5}$. What is the correct sum?

    $\frac{5}{6}$. Error: added denominators; correct method uses LCD 6.

46. What is $2\frac{3}{4}+1\frac{2}{3}$? Give the answer as a simplified mixed number.

    $4\frac{5}{12}$. Convert to improper fractions, add using LCD 12, then simplify.

47. Identify the common denominator used in $\frac{3}{4}+\frac{2}{3}=\frac{9}{12}+\frac{8}{12}$.

    $12$. $12$ is the LCD of $4$ and $3$.

48. What is the least common denominator (LCD) of $\frac{1}{4}$ and $\frac{1}{10}$?

    $20$. LCD is the smallest number divisible by both 4 and 10.

49. State the general formula for $\frac{a}{b}+\frac{c}{d}$ using a common denominator.

    $\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$. Cross-multiply and add numerators over the product of denominators.

50. Identify the equivalent fraction: $\frac{3}{5}=\frac{?}{20}$.

    $\frac{12}{20}$. Multiply numerator and denominator by 4 since $5×4=20$.

51. What is $\frac{2}{9}+\frac{1}{6}$? Give the answer in simplest form.

    $\frac{7}{18}$. Convert to $\frac{4}{18}+\frac{3}{18}$ using LCD 18.

52. What is the least common denominator (LCD) of $\frac{1}{6}$ and $\frac{1}{8}$?

    $24$. LCD is the smallest number divisible by both 6 and 8.

53. What is $\frac{5}{6}-\frac{1}{4}$? Give the answer in simplest form.

    $\frac{7}{12}$. Convert to $\frac{10}{12}-\frac{3}{12}$ using LCD 12.

54. Which fraction is equivalent to $\frac{2}{3}$ with denominator $12$?

    $\frac{8}{12}$. Multiply numerator and denominator by 4 to get denominator 12.

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