Adding and subtracting mixed numbers involves working with whole numbers and fractions together. You can convert mixed numbers to improper fractions, find a common denominator, and then add or subtract the numerators. Finally, simplify your answer and convert it back to a mixed number when appropriate. These practice problems include common denominators, unlike denominators, regrouping, and word problems.
Practice Problems
\(\textbf{1)}\) \(3 \frac{2}{3}+1 \frac{1}{5}\)
The answer is \(4\frac{13}{15}\)
\(\,\,\,\,\,3\frac{2}{3}+1\frac{1}{5}\)
\(\,\,\,\,\,\frac{11}{3}+\frac{6}{5}\)
\(\,\,\,\,\,\frac{55}{15}+\frac{18}{15}\)
\(\,\,\,\,\,\frac{55+18}{15}\)
\(\,\,\,\,\,\frac{73}{15}\)
\(\,\,\,\,\,4\frac{13}{15}\)
\(\,\,\,\,\,3\frac{2}{3}+1\frac{1}{5}\)
\(\,\,\,\,\,\frac{11}{3}+\frac{6}{5}\)
\(\,\,\,\,\,\frac{55}{15}+\frac{18}{15}\)
\(\,\,\,\,\,\frac{55+18}{15}\)
\(\,\,\,\,\,\frac{73}{15}\)
\(\,\,\,\,\,4\frac{13}{15}\)
\(\textbf{2)}\) \(4 \frac{3}{4}+2 \frac{2}{3}\)
The answer is \(7\frac{5}{12}\)
\(\,\,\,\,\,4\frac{3}{4}+2\frac{2}{3}\)
\(\,\,\,\,\,\frac{19}{4}+\frac{8}{3}\)
\(\,\,\,\,\,\frac{57}{12}+\frac{32}{12}\)
\(\,\,\,\,\,\frac{89}{12}\)
\(\,\,\,\,\,7\frac{5}{12}\)
\(\,\,\,\,\,4\frac{3}{4}+2\frac{2}{3}\)
\(\,\,\,\,\,\frac{19}{4}+\frac{8}{3}\)
\(\,\,\,\,\,\frac{57}{12}+\frac{32}{12}\)
\(\,\,\,\,\,\frac{89}{12}\)
\(\,\,\,\,\,7\frac{5}{12}\)
\(\textbf{3)}\) \(1 \frac{5}{6}-1 \frac{1}{3}\)
The answer is \(\frac{1}{2}\)
\(\,\,\,\,\,1\frac{5}{6}-1\frac{1}{3}\)
\(\,\,\,\,\,\frac{11}{6}-\frac{4}{3}\)
\(\,\,\,\,\,\frac{11}{6}-\frac{8}{6}\)
\(\,\,\,\,\,\frac{3}{6}\)
\(\,\,\,\,\,\frac{1}{2}\)
\(\,\,\,\,\,1\frac{5}{6}-1\frac{1}{3}\)
\(\,\,\,\,\,\frac{11}{6}-\frac{4}{3}\)
\(\,\,\,\,\,\frac{11}{6}-\frac{8}{6}\)
\(\,\,\,\,\,\frac{3}{6}\)
\(\,\,\,\,\,\frac{1}{2}\)
\(\textbf{4)}\) \(3 \frac{5}{8}-1 \frac{3}{8}\)
The answer is \(2\frac{1}{4}\)
\(\,\,\,\,\,3\frac{5}{8}-1\frac{3}{8}\)
\(\,\,\,\,\,\frac{29}{8}-\frac{11}{8}\)
\(\,\,\,\,\,\frac{18}{8}\)
\(\,\,\,\,\,\frac{9}{4}\)
\(\,\,\,\,\,2\frac{1}{4}\)
\(\,\,\,\,\,3\frac{5}{8}-1\frac{3}{8}\)
\(\,\,\,\,\,\frac{29}{8}-\frac{11}{8}\)
\(\,\,\,\,\,\frac{18}{8}\)
\(\,\,\,\,\,\frac{9}{4}\)
\(\,\,\,\,\,2\frac{1}{4}\)
\(\textbf{5)}\) \(4 \frac{2}{3}+3 \frac{2}{3}\)
The answer is \(8\frac{1}{3}\)
\(\,\,\,\,\,4\frac{2}{3}+3\frac{2}{3}\)
\(\,\,\,\,\,\frac{14}{3}+\frac{11}{3}\)
\(\,\,\,\,\,\frac{25}{3}\)
\(\,\,\,\,\,8\frac{1}{3}\)
\(\,\,\,\,\,4\frac{2}{3}+3\frac{2}{3}\)
\(\,\,\,\,\,\frac{14}{3}+\frac{11}{3}\)
\(\,\,\,\,\,\frac{25}{3}\)
\(\,\,\,\,\,8\frac{1}{3}\)
\(\textbf{6)}\) \(5 \frac{1}{5}-1 \frac{3}{5}\)
The answer is \(3\frac{3}{5}\)
\(\,\,\,\,\,5\frac{1}{5}-1\frac{3}{5}\)
\(\,\,\,\,\,\frac{26}{5}-\frac{8}{5}\)
\(\,\,\,\,\,\frac{18}{5}\)
\(\,\,\,\,\,3\frac{3}{5}\)
\(\,\,\,\,\,5\frac{1}{5}-1\frac{3}{5}\)
\(\,\,\,\,\,\frac{26}{5}-\frac{8}{5}\)
\(\,\,\,\,\,\frac{18}{5}\)
\(\,\,\,\,\,3\frac{3}{5}\)
\(\textbf{7)}\) \(2 \frac{1}{3}+4 \frac{2}{3}\)
The answer is \(7\)
\(\,\,\,\,\,2\frac{1}{3}+4\frac{2}{3}\)
\(\,\,\,\,\,\frac{7}{3}+\frac{14}{3}\)
\(\,\,\,\,\,\frac{21}{3}\)
\(\,\,\,\,\,7\)
\(\,\,\,\,\,2\frac{1}{3}+4\frac{2}{3}\)
\(\,\,\,\,\,\frac{7}{3}+\frac{14}{3}\)
\(\,\,\,\,\,\frac{21}{3}\)
\(\,\,\,\,\,7\)
\(\textbf{8)}\) \(3 \frac{1}{8}+1 \frac{3}{4}\)
The answer is \(4\frac{7}{8}\)
\(\,\,\,\,\,3\frac{1}{8}+1\frac{3}{4}\)
\(\,\,\,\,\,\frac{25}{8}+\frac{7}{4}\)
\(\,\,\,\,\,\frac{25}{8}+\frac{14}{8}\)
\(\,\,\,\,\,\frac{39}{8}\)
\(\,\,\,\,\,4\frac{7}{8}\)
\(\,\,\,\,\,3\frac{1}{8}+1\frac{3}{4}\)
\(\,\,\,\,\,\frac{25}{8}+\frac{7}{4}\)
\(\,\,\,\,\,\frac{25}{8}+\frac{14}{8}\)
\(\,\,\,\,\,\frac{39}{8}\)
\(\,\,\,\,\,4\frac{7}{8}\)
\(\textbf{9)}\) \(3 \frac{1}{3}-2 \frac{1}{3}\)
The answer is \(1\)
\(\,\,\,\,\,3\frac{1}{3}-2\frac{1}{3}\)
\(\,\,\,\,\,\frac{10}{3}-\frac{7}{3}\)
\(\,\,\,\,\,\frac{3}{3}\)
\(\,\,\,\,\,1\)
\(\,\,\,\,\,3\frac{1}{3}-2\frac{1}{3}\)
\(\,\,\,\,\,\frac{10}{3}-\frac{7}{3}\)
\(\,\,\,\,\,\frac{3}{3}\)
\(\,\,\,\,\,1\)
\(\textbf{10)}\) \(2 \frac{1}{4}+1 \frac{1}{2}\)
The answer is \(3\frac{3}{4}\)
\(\,\,\,\,\,2\frac{1}{4}+1\frac{1}{2}\)
\(\,\,\,\,\,\frac{9}{4}+\frac{3}{2}\)
\(\,\,\,\,\,\frac{9}{4}+\frac{6}{4}\)
\(\,\,\,\,\,\frac{15}{4}\)
\(\,\,\,\,\,3\frac{3}{4}\)
\(\,\,\,\,\,2\frac{1}{4}+1\frac{1}{2}\)
\(\,\,\,\,\,\frac{9}{4}+\frac{3}{2}\)
\(\,\,\,\,\,\frac{9}{4}+\frac{6}{4}\)
\(\,\,\,\,\,\frac{15}{4}\)
\(\,\,\,\,\,3\frac{3}{4}\)
\(\textbf{11)}\) \(6 \frac{3}{4}-2 \frac{1}{2}\)
The answer is \(4\frac{1}{4}\)
\(\,\,\,\,\,6\frac{3}{4}-2\frac{1}{2}\)
\(\,\,\,\,\,\frac{27}{4}-\frac{5}{2}\)
\(\,\,\,\,\,\frac{27}{4}-\frac{10}{4}\)
\(\,\,\,\,\,\frac{17}{4}\)
\(\,\,\,\,\,4\frac{1}{4}\)
\(\,\,\,\,\,6\frac{3}{4}-2\frac{1}{2}\)
\(\,\,\,\,\,\frac{27}{4}-\frac{5}{2}\)
\(\,\,\,\,\,\frac{27}{4}-\frac{10}{4}\)
\(\,\,\,\,\,\frac{17}{4}\)
\(\,\,\,\,\,4\frac{1}{4}\)
\(\textbf{12)}\) \(2 \frac{5}{6}+3 \frac{3}{4}\)
The answer is \(6\frac{7}{12}\)
\(\,\,\,\,\,2\frac{5}{6}+3\frac{3}{4}\)
\(\,\,\,\,\,\frac{17}{6}+\frac{15}{4}\)
\(\,\,\,\,\,\frac{34}{12}+\frac{45}{12}\)
\(\,\,\,\,\,\frac{79}{12}\)
\(\,\,\,\,\,6\frac{7}{12}\)
\(\,\,\,\,\,2\frac{5}{6}+3\frac{3}{4}\)
\(\,\,\,\,\,\frac{17}{6}+\frac{15}{4}\)
\(\,\,\,\,\,\frac{34}{12}+\frac{45}{12}\)
\(\,\,\,\,\,\frac{79}{12}\)
\(\,\,\,\,\,6\frac{7}{12}\)
\(\textbf{13)}\) \(7 \frac{1}{3}-2 \frac{5}{6}\)
The answer is \(4\frac{1}{2}\)
\(\,\,\,\,\,7\frac{1}{3}-2\frac{5}{6}\)
\(\,\,\,\,\,\frac{22}{3}-\frac{17}{6}\)
\(\,\,\,\,\,\frac{44}{6}-\frac{17}{6}\)
\(\,\,\,\,\,\frac{27}{6}\)
\(\,\,\,\,\,\frac{9}{2}\)
\(\,\,\,\,\,4\frac{1}{2}\)
\(\,\,\,\,\,7\frac{1}{3}-2\frac{5}{6}\)
\(\,\,\,\,\,\frac{22}{3}-\frac{17}{6}\)
\(\,\,\,\,\,\frac{44}{6}-\frac{17}{6}\)
\(\,\,\,\,\,\frac{27}{6}\)
\(\,\,\,\,\,\frac{9}{2}\)
\(\,\,\,\,\,4\frac{1}{2}\)
\(\textbf{14)}\) \(1 \frac{7}{10}+2 \frac{9}{10}\)
The answer is \(4\frac{3}{5}\)
\(\,\,\,\,\,1\frac{7}{10}+2\frac{9}{10}\)
\(\,\,\,\,\,\frac{17}{10}+\frac{29}{10}\)
\(\,\,\,\,\,\frac{46}{10}\)
\(\,\,\,\,\,\frac{23}{5}\)
\(\,\,\,\,\,4\frac{3}{5}\)
\(\,\,\,\,\,1\frac{7}{10}+2\frac{9}{10}\)
\(\,\,\,\,\,\frac{17}{10}+\frac{29}{10}\)
\(\,\,\,\,\,\frac{46}{10}\)
\(\,\,\,\,\,\frac{23}{5}\)
\(\,\,\,\,\,4\frac{3}{5}\)
\(\textbf{15)}\) \(8 \frac{1}{4}-3 \frac{7}{8}\)
The answer is \(4\frac{3}{8}\)
\(\,\,\,\,\,8\frac{1}{4}-3\frac{7}{8}\)
\(\,\,\,\,\,\frac{33}{4}-\frac{31}{8}\)
\(\,\,\,\,\,\frac{66}{8}-\frac{31}{8}\)
\(\,\,\,\,\,\frac{35}{8}\)
\(\,\,\,\,\,4\frac{3}{8}\)
\(\,\,\,\,\,8\frac{1}{4}-3\frac{7}{8}\)
\(\,\,\,\,\,\frac{33}{4}-\frac{31}{8}\)
\(\,\,\,\,\,\frac{66}{8}-\frac{31}{8}\)
\(\,\,\,\,\,\frac{35}{8}\)
\(\,\,\,\,\,4\frac{3}{8}\)
\(\textbf{16)}\) \(4 \frac{5}{12}+2 \frac{1}{6}\)
The answer is \(6\frac{7}{12}\)
\(\,\,\,\,\,4\frac{5}{12}+2\frac{1}{6}\)
\(\,\,\,\,\,\frac{53}{12}+\frac{13}{6}\)
\(\,\,\,\,\,\frac{53}{12}+\frac{26}{12}\)
\(\,\,\,\,\,\frac{79}{12}\)
\(\,\,\,\,\,6\frac{7}{12}\)
\(\,\,\,\,\,4\frac{5}{12}+2\frac{1}{6}\)
\(\,\,\,\,\,\frac{53}{12}+\frac{13}{6}\)
\(\,\,\,\,\,\frac{53}{12}+\frac{26}{12}\)
\(\,\,\,\,\,\frac{79}{12}\)
\(\,\,\,\,\,6\frac{7}{12}\)
\(\textbf{17)}\) \(5 \frac{2}{9}-1 \frac{7}{9}\)
The answer is \(3\frac{4}{9}\)
\(\,\,\,\,\,5\frac{2}{9}-1\frac{7}{9}\)
\(\,\,\,\,\,\frac{47}{9}-\frac{16}{9}\)
\(\,\,\,\,\,\frac{31}{9}\)
\(\,\,\,\,\,3\frac{4}{9}\)
\(\,\,\,\,\,5\frac{2}{9}-1\frac{7}{9}\)
\(\,\,\,\,\,\frac{47}{9}-\frac{16}{9}\)
\(\,\,\,\,\,\frac{31}{9}\)
\(\,\,\,\,\,3\frac{4}{9}\)
\(\textbf{18)}\) \(3 \frac{3}{5}+2 \frac{7}{10}\)
The answer is \(6\frac{3}{10}\)
\(\,\,\,\,\,3\frac{3}{5}+2\frac{7}{10}\)
\(\,\,\,\,\,\frac{18}{5}+\frac{27}{10}\)
\(\,\,\,\,\,\frac{36}{10}+\frac{27}{10}\)
\(\,\,\,\,\,\frac{63}{10}\)
\(\,\,\,\,\,6\frac{3}{10}\)
\(\,\,\,\,\,3\frac{3}{5}+2\frac{7}{10}\)
\(\,\,\,\,\,\frac{18}{5}+\frac{27}{10}\)
\(\,\,\,\,\,\frac{36}{10}+\frac{27}{10}\)
\(\,\,\,\,\,\frac{63}{10}\)
\(\,\,\,\,\,6\frac{3}{10}\)
\(\textbf{19)}\) \(9 \frac{1}{2}-4 \frac{2}{3}\)
The answer is \(4\frac{5}{6}\)
\(\,\,\,\,\,9\frac{1}{2}-4\frac{2}{3}\)
\(\,\,\,\,\,\frac{19}{2}-\frac{14}{3}\)
\(\,\,\,\,\,\frac{57}{6}-\frac{28}{6}\)
\(\,\,\,\,\,\frac{29}{6}\)
\(\,\,\,\,\,4\frac{5}{6}\)
\(\,\,\,\,\,9\frac{1}{2}-4\frac{2}{3}\)
\(\,\,\,\,\,\frac{19}{2}-\frac{14}{3}\)
\(\,\,\,\,\,\frac{57}{6}-\frac{28}{6}\)
\(\,\,\,\,\,\frac{29}{6}\)
\(\,\,\,\,\,4\frac{5}{6}\)
\(\textbf{20)}\) \(2 \frac{3}{4}+1 \frac{2}{3}+3 \frac{1}{6}\)
The answer is \(7\frac{7}{12}\)
\(\,\,\,\,\,2\frac{3}{4}+1\frac{2}{3}+3\frac{1}{6}\)
\(\,\,\,\,\,\frac{11}{4}+\frac{5}{3}+\frac{19}{6}\)
\(\,\,\,\,\,\frac{33}{12}+\frac{20}{12}+\frac{38}{12}\)
\(\,\,\,\,\,\frac{91}{12}\)
\(\,\,\,\,\,7\frac{7}{12}\)
\(\,\,\,\,\,2\frac{3}{4}+1\frac{2}{3}+3\frac{1}{6}\)
\(\,\,\,\,\,\frac{11}{4}+\frac{5}{3}+\frac{19}{6}\)
\(\,\,\,\,\,\frac{33}{12}+\frac{20}{12}+\frac{38}{12}\)
\(\,\,\,\,\,\frac{91}{12}\)
\(\,\,\,\,\,7\frac{7}{12}\)
Challenge Problems
\(\textbf{21)}\)\(\text{Evaluate } x-y \text{ if } x=2\frac{3}{5} \text{ and } y=1\frac{1}{3}\)
The answer is \(1\frac{4}{15}\)
\(\,\,\,\,\,x-y\)
\(\,\,\,\,\,2\frac{3}{5}-1\frac{1}{3}\)
\(\,\,\,\,\,\frac{13}{5}-\frac{4}{3}\)
\(\,\,\,\,\,\frac{39}{15}-\frac{20}{15}\)
\(\,\,\,\,\,\frac{19}{15}\)
\(\,\,\,\,\,1\frac{4}{15}\)
\(\,\,\,\,\,x-y\)
\(\,\,\,\,\,2\frac{3}{5}-1\frac{1}{3}\)
\(\,\,\,\,\,\frac{13}{5}-\frac{4}{3}\)
\(\,\,\,\,\,\frac{39}{15}-\frac{20}{15}\)
\(\,\,\,\,\,\frac{19}{15}\)
\(\,\,\,\,\,1\frac{4}{15}\)
See Related Pages\(\)
\(\bullet\text{ Reducing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{9}{15}=\frac{3}{5}…\)
\(\bullet\text{ Comparing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{3}{4} \bigcirc \frac{4}{5}…\)
\(\bullet\text{ Adding and Subtracting Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{4}{5}+\frac{2}{3}…\)
\(\bullet\text{ Multiplying Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}\times\frac{5}{8}…\)
\(\bullet\text{ Dividing Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{7}\div\frac{1}{5}…\)
\(\bullet\text{ Improper Fractions and Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,\frac{35}{4}=8\frac{3}{4}…\)
\(\bullet\text{ Dividing Mixed Numbers}\)
\(\,\,\,\,\,\,\,\,3 \frac{2}{3}÷1 \frac{1}{5}…\)