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Adding and Subtracting Mixed Numbers

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Adding and Subtracting Mixed Numbers: Difficult Problems with Solutions

Problem 1

[tex]1\frac{1}{6} + 1\frac{3}{4} =[/tex]

$2 \frac{7}{8}$

$2 \frac{11}{12}$

$2 \frac{8}{10}$

$2 \frac{9}{12}$

Solution:
[tex]1\frac{1}{6} + 1\frac{3}{4} = (1+1) + ( \frac{1}{6} + \frac{3}{4} ) = 2 + \frac{2 + 9}{12} = 2 + \frac{11}{12}=2\frac{11}{12}[/tex]

Problem 2

[tex]2\frac{2}{5} - 1\frac{1}{2} =[/tex]

Solution:
[tex]2\frac{2}{5} - 1\frac{1}{2} = (2-1) + ( \frac{2}{5} - \frac{1}{2} ) = 1 + \frac{4 - 5}{10} = 1 - \frac{1}{10} = \frac{9}{10}[/tex]

Problem 3

[tex]2\frac{11}{13} - 1\frac{2}{9} =[/tex]

$1 \frac{73}{117}$

$1 \frac{19}{27}$

$1 \frac{27}{56}$

$\frac{73}{117}$

Solution:
[tex]2\frac{11}{13} - 1\frac{2}{9} = (2 - 1) + ( \frac{11}{13} - \frac{2}{9} ) = 1 + \frac{99 - 26}{117} = 1 + \frac{73}{117} = 1 \frac{73}{117}[/tex]

Problem 4

[tex]5\frac{1}{3} + 3\frac{3}{5} =[/tex]

$8\frac{4}{15}$

$8\frac{12}{15}$

$8\frac{14}{15}$

$8\frac{4}{8}$

Solution:
[tex]5\frac{1}{3} + 3\frac{3}{5} = (5 + 3) + ( \frac{1}{3} + \frac{3}{5} ) = 8 + \frac{5 + 9}{15} = 8 + \frac{14}{15} = \frac{134}{15}[/tex]

Problem 5

[tex]3\frac{7}{9} - 3\frac{1}{4} =[/tex]

Solution:
[tex]3\frac{7}{9} - 3\frac{1}{4} = (3 - 3) + ( \frac{7}{9} - \frac{1}{4} ) = 0 + \frac{28 - 9}{36} = \frac{19}{36}[/tex]

Problem 6

[tex]2\frac{3}{5} + 2\frac{1}{8} =[/tex]

$4\frac{18}{25}$

$4\frac{1}{3}$

$4\frac{4}{12}$

$4\frac{29}{40}$

Solution:
[tex]2\frac{3}{5} + 2\frac{1}{8} = (2 + 2) + ( \frac{3}{5} + \frac{1}{8} ) = 4 + \frac{24 + 5}{40} = 4 + \frac{29}{40} = 4\frac{29}{40}[/tex]

Problem 7

[tex]7\frac{1}{3} - 2\frac{11}{12} =[/tex]

$\frac{53}{12}$

$5\frac{21}{36}$

$4\frac{21}{36}$

$5\frac{7}{12}$

Solution:
[tex]7\frac{1}{3} - 2\frac{11}{12} = (7 - 2) + ( \frac{1}{3} - \frac{11}{12} ) = 5 + \frac{12 - 33}{36} = 5 - \frac{21}{36} = \frac{159}{36} = \frac{53}{12}[/tex]

Problem 8

[tex]1\frac{4}{7} + 5\frac{1}{4} =[/tex]

$6\frac{5}{11}$

$6\frac{23}{28}$

$6\frac{5}{28}$

$6\frac{21}{28}$

Solution:
[tex]1\frac{4}{7} + 5\frac{1}{4} = (1 + 5) + ( \frac{4}{7} + \frac{1}{4} ) = 6 + \frac{16 + 7}{28} = 6 + \frac{23}{28} = 6\frac{23}{28}[/tex]

Problem 9

[tex]4\frac{4}{5} - 2\frac{5}{6} = [/tex]

$1\frac{1}{5}$

$\frac{58}{30}$

$\frac{29}{30}$

$1\frac{29}{30}$

Solution:
[tex]4\frac{4}{5} - 2\frac{5}{6} = (4 - 2) + (\frac{4}{5} - \frac{5}{6}) = 2 + \frac{24 - 25}{30} = 2 - \frac{1}{30} = 1 + \frac{30}{30} - \frac{1}{30} = 1+\frac{29}{30}=1\frac{29}{30}[/tex]

Problem 10

[tex]5\frac{1}{5} - 2\frac{3}{10} =[/tex]

$3\frac{1}{10}$

$3\frac{9}{10}$

$2\frac{9}{10}$

$3\frac{1}{5}$

Solution:
[tex]5\frac{1}{5} - 2\frac{3}{10} = (5 - 2) + (\frac{1}{5} - \frac{3}{10}) = 3 + \frac{2 - 3}{10} = 3 - \frac{1}{10} = 2 + \frac{10}{10}-\frac{1}{10}=2+\frac{9}{10}=2\frac{9}{10}[/tex]

Problem 11

[tex]2\frac{3}{4} + 4\frac{5}{6} = [/tex]

$7 \frac{7}{12}$

$6 \frac{14}{24}$

$6 \frac{8}{10}$

$7 \frac{1}{2}$

Solution:
[tex]2\frac{3}{4} + 4\frac{5}{6} = (2 + 4) + (\frac{3}{4} + \frac{5}{6}) = 6 + \frac{18 + 20}{24} = 6 + \frac{38}{24} = 6 + \frac{24}{24} + \frac{14}{24} = 7 + \frac{14}{24} = 7 + \frac{7}{12} = = 7 \frac{7}{12}[/tex]

Problem 12

[tex]6\frac{3}{8} - 3\frac{3}{4} = [/tex]

$3\frac{5}{8}$

$3\frac{1}{4}$

$3\frac{1}{4}$

$2\frac{5}{8}$

Solution:
[tex]6\frac{3}{8} - 3\frac{3}{4} = (6 - 3) + (\frac{3}{8} - \frac{3}{4}) = 3 + \frac{3}{8} - \frac{6}{8} = 2 + \frac{8}{8} + \frac{3}{8} - \frac{6}{8} =2 + \frac{5}{8}=2\frac{5}{8}[/tex]

Problem 13

[tex]1\frac{3}{10} + 4\frac{5}{6} =[/tex]

$5\frac{2}{15}$

$6\frac{2}{15}$

$6\frac{2}{30}$

$5\frac{1}{2}$

Solution:
[tex]1\frac{3}{10} + 4\frac{5}{6} = (1 + 4) + (\frac{3}{10} + \frac{5}{6}) = 5 + \frac{9 + 25}{30} = 5 + \frac{34}{30} = 5+ \frac{30}{30}+\frac{4}{30}=6+\frac{4}{30}=6\frac{2}{15}[/tex]

Problem 14

[tex]2\frac{4}{15} + 6\frac{5}{9} =[/tex]

$8\frac{9}{24}$

$8\frac{24}{35}$

$8\frac{37}{90}$

$8\frac{37}{45}$

Solution:
[tex]2\frac{4}{15} + 6\frac{5}{9} = (2 + 6) + (\frac{4}{15} + \frac{5}{9}) = 8 + \frac{12 + 25}{45} = 8 + \frac{37}{45}=8\frac{37}{45}[/tex]

Problem 15

[tex]5\frac{7}{20} - 2\frac{3}{14} =[/tex]

$2\frac{19}{140}$

$3\frac{19}{120}$

$\frac{439}{140}$

$3\frac{17}{140}$

Solution:
[tex]5\frac{7}{20} - 2\frac{3}{14} = (5 - 2) + (\frac{7}{20} - \frac{3}{14}) = 3 + \frac{49 - 30}{140} = 3 + \frac{19}{140} = \frac{439}{140}[/tex]

Problem 16

[tex]1\frac{1}{2} + 3\frac{5}{18} =[/tex]

$4\frac{15}{18}$

$4\frac{7}{9}$

$4\frac{8}{9}$

$4\frac{3}{10}$

Solution:
[tex]1\frac{1}{2} + 3\frac{5}{18} = (1 + 3) + (\frac{1}{2} + \frac{5}{18}) = 4 + \frac{9 + 5}{18} = 4 + \frac{14}{18} = 4 + \frac{7}{9}=4\frac{7}{9}[/tex]

Problem 17

[tex]2\frac{4}{25} - 1\frac{2}{21} =[/tex]

$\frac{559}{525}$

$\frac{34}{525}$

$2\frac{34}{525}$

$3\frac{34}{525}$

Solution:
[tex]2\frac{4}{25} - 1\frac{2}{21} = (2 - 1) + (\frac{4}{25} - \frac{2}{21}) = 1 + \frac{84 - 50}{525} = 1 + \frac{34}{525} = \frac{525}{525} + \frac{34}{525} = \frac{559}{525}[/tex]

Problem 18

[tex]3\frac{4}{5} + 1\frac{2}{13} =[/tex]

$4\frac{54}{65}$

$4\frac{61}{65}$

$4\frac{6}{18}$

$4\frac{62}{65}$

Solution:
[tex]3\frac{4}{5} + 1\frac{2}{13} = (3 + 1) + ( \frac{4}{5} + \frac{2}{13} ) = 4 + \frac{52 + 10}{65} = 4 + \frac{62}{65} = 4\frac{62}{65}[/tex]

Problem 19

[tex]5\frac{5}{16} - 1\frac{3}{10} =[/tex]

$4\frac{2}{80}$

$4\frac{5}{80}$

$4\frac{1}{80}$

$4\frac{1}{32}$

Solution:
[tex]5\frac{5}{16} - 1\frac{3}{10} = (5 - 1) + (\frac{5}{16} - \frac{3}{10}) = 4 + \frac{25 - 24}{80} = 4 + \frac{1}{80} = 4\frac{1}{80}[/tex]

Problem 20

[tex]2\frac{1}{11} + 5\frac{4}{17} =[/tex]

$7\frac{61}{187}$

$7\frac{51}{187}$

$7\frac{56}{187}$

$7\frac{71}{187}$

Solution:
[tex]2\frac{1}{11} + 5\frac{4}{17} = (2 + 5) + (\frac{1}{11} + \frac{4}{17}) = 7 + \frac{17 + 44}{187} = 7 + \frac{61}{187} = 7\frac{61}{187}[/tex]

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