How to Subtract Mixed Numbers

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Subtracting mixed numbers means subtracting whole-number parts and fraction parts. When the top fraction is smaller than the fraction being subtracted, borrow \(1\) from the whole number and add it to the fraction as one whole.

Steps to Subtract Mixed Numbers

Rewrite the fractions with a common denominator.
Borrow from the first whole number if the first fraction is smaller.
Subtract the whole numbers and subtract the fractions.
Simplify the final fraction.

Example: \(6\frac{1}{4}-2\frac{5}{8}=5\frac{10}{8}-2\frac{5}{8}=3\frac{5}{8}\).

Subtract Mixed Numbers

Think of this lesson as more than a rule to memorize. Subtract Mixed Numbers is about number sense, equivalent forms, and careful arithmetic. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Fractions compare a part to a whole. Keep track of the numerator, denominator, and whether the pieces are the same size before adding, subtracting, or simplifying.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Read what is given and what is being asked.
Choose the rule that connects them.
Substitute carefully and simplify in small steps.
Check the final answer against the original question.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Subtracting Mixed Numbers

1) \(4\frac{3}{5} - 1\frac{1}{5} =\)

2) \(6\frac{7}{8} - 2\frac{3}{8} =\)

3) \(8\frac{5}{6} - 3\frac{1}{3} =\)

4) \(9\frac{7}{10} - 4\frac{3}{5} =\)

5) \(7\frac{1}{4} - 2\frac{5}{6} =\)

6) \(10\frac{2}{9} - 3\frac{5}{12} =\)

7) \(12\frac{3}{8} - 5\frac{7}{10} =\)

8) \(15\frac{5}{6} - 9\frac{11}{14} =\)

9) \(18\frac{7}{12} - 6\frac{5}{18} =\)

10) \(20\frac{11}{15} - 13\frac{7}{10} =\)

11) \(24\frac{5}{16} - 8\frac{11}{24} =\)

12) \(30\frac{13}{20} - 19\frac{7}{12} =\)

13) \(35\frac{17}{21} - 16\frac{19}{28} =\)

14) \(42\frac{23}{30} - 27\frac{17}{20} =\)

15) \(50\frac{29}{36} - 31\frac{13}{18} =\)

16) \(61\frac{31}{40} - 28\frac{17}{32} =\)

17) \(75\frac{37}{45} - 44\frac{29}{60} =\)

18) \(90\frac{41}{56} - 58\frac{33}{70} =\)

19) \(125\frac{47}{72} - 88\frac{55}{96} =\)

20) \(150\frac{59}{84} - 97\frac{65}{112} =\)

Answers

1) \(4\frac{3}{5} - 1\frac{1}{5} = \color{red}{3\frac{2}{5}}\)

GCF(10,25) = 5

Solution:
Separate the whole-number and fraction parts: \((4 - 1) + (\frac{3}{5} - \frac{1}{5})\).
Use the common denominator \(25\): \(\frac{3}{5}=\frac{15}{25}\) and \(\frac{1}{5}=\frac{5}{25}\).
Compute the whole-number part: \(4-1=3\).
Compute the fraction part: \(\frac{15}{25} - \frac{5}{25}=\frac{10}{25}\), which simplifies to \(\frac{2}{5}\).
Combine the parts: \(3\frac{2}{5}\).

2) \(6\frac{7}{8} - 2\frac{3}{8} = \color{red}{4\frac{1}{2}}\)

GCF(32,64) = 32

Solution:
Separate the whole-number and fraction parts: \((6 - 2) + (\frac{7}{8} - \frac{3}{8})\).
Use the common denominator \(64\): \(\frac{7}{8}=\frac{56}{64}\) and \(\frac{3}{8}=\frac{24}{64}\).
Compute the whole-number part: \(6-2=4\).
Compute the fraction part: \(\frac{56}{64} - \frac{24}{64}=\frac{32}{64}\), which simplifies to \(\frac{1}{2}\).
Combine the parts: \(4\frac{1}{2}\).

3) \(8\frac{5}{6} - 3\frac{1}{3} = \color{red}{5\frac{1}{2}}\)

GCF(9,18) = 9

Solution:
Separate the whole-number and fraction parts: \((8 - 3) + (\frac{5}{6} - \frac{1}{3})\).
Use the common denominator \(18\): \(\frac{5}{6}=\frac{15}{18}\) and \(\frac{1}{3}=\frac{6}{18}\).
Compute the whole-number part: \(8-3=5\).
Compute the fraction part: \(\frac{15}{18} - \frac{6}{18}=\frac{9}{18}\), which simplifies to \(\frac{1}{2}\).
Combine the parts: \(5\frac{1}{2}\).

4) \(9\frac{7}{10} - 4\frac{3}{5} = \color{red}{5\frac{1}{10}}\)

GCF(5,50) = 5

Solution:
Separate the whole-number and fraction parts: \((9 - 4) + (\frac{7}{10} - \frac{3}{5})\).
Use the common denominator \(50\): \(\frac{7}{10}=\frac{35}{50}\) and \(\frac{3}{5}=\frac{30}{50}\).
Compute the whole-number part: \(9-4=5\).
Compute the fraction part: \(\frac{35}{50} - \frac{30}{50}=\frac{5}{50}\), which simplifies to \(\frac{1}{10}\).
Combine the parts: \(5\frac{1}{10}\).

5) \(7\frac{1}{4} - 2\frac{5}{6} = \color{red}{4\frac{5}{12}}\)

GCF(10,24) = 2

Solution:
Separate the whole-number and fraction parts: \((7 - 2) + (\frac{1}{4} - \frac{5}{6})\).
Use the common denominator \(24\): \(\frac{1}{4}=\frac{6}{24}\) and \(\frac{5}{6}=\frac{20}{24}\). Since \(\frac{6}{24}\) is smaller than \(\frac{20}{24}\), borrow \(1\) from \(7\) so the first fraction becomes \(\frac{30}{24}\).
Compute the whole-number part: \(7-1-2=4\).
Compute the fraction part: \(\frac{30}{24} - \frac{20}{24}=\frac{10}{24}\), which simplifies to \(\frac{5}{12}\).
Combine the parts: \(4\frac{5}{12}\).

6) \(10\frac{2}{9} - 3\frac{5}{12} = \color{red}{6\frac{29}{36}}\)

GCF(87,108) = 3

Solution:
Separate the whole-number and fraction parts: \((10 - 3) + (\frac{2}{9} - \frac{5}{12})\).
Use the common denominator \(108\): \(\frac{2}{9}=\frac{24}{108}\) and \(\frac{5}{12}=\frac{45}{108}\). Since \(\frac{24}{108}\) is smaller than \(\frac{45}{108}\), borrow \(1\) from \(10\) so the first fraction becomes \(\frac{132}{108}\).
Compute the whole-number part: \(10-1-3=6\).
Compute the fraction part: \(\frac{132}{108} - \frac{45}{108}=\frac{87}{108}\), which simplifies to \(\frac{29}{36}\).
Combine the parts: \(6\frac{29}{36}\).

7) \(12\frac{3}{8} - 5\frac{7}{10} = \color{red}{6\frac{27}{40}}\)

GCF(54,80) = 2

Solution:
Separate the whole-number and fraction parts: \((12 - 5) + (\frac{3}{8} - \frac{7}{10})\).
Use the common denominator \(80\): \(\frac{3}{8}=\frac{30}{80}\) and \(\frac{7}{10}=\frac{56}{80}\). Since \(\frac{30}{80}\) is smaller than \(\frac{56}{80}\), borrow \(1\) from \(12\) so the first fraction becomes \(\frac{110}{80}\).
Compute the whole-number part: \(12-1-5=6\).
Compute the fraction part: \(\frac{110}{80} - \frac{56}{80}=\frac{54}{80}\), which simplifies to \(\frac{27}{40}\).
Combine the parts: \(6\frac{27}{40}\).

8) \(15\frac{5}{6} - 9\frac{11}{14} = \color{red}{6\frac{1}{21}}\)

GCF(4,84) = 4

Solution:
Separate the whole-number and fraction parts: \((15 - 9) + (\frac{5}{6} - \frac{11}{14})\).
Use the common denominator \(84\): \(\frac{5}{6}=\frac{70}{84}\) and \(\frac{11}{14}=\frac{66}{84}\).
Compute the whole-number part: \(15-9=6\).
Compute the fraction part: \(\frac{70}{84} - \frac{66}{84}=\frac{4}{84}\), which simplifies to \(\frac{1}{21}\).
Combine the parts: \(6\frac{1}{21}\).

9) \(18\frac{7}{12} - 6\frac{5}{18} = \color{red}{12\frac{11}{36}}\)

GCF(66,216) = 6

Solution:
Separate the whole-number and fraction parts: \((18 - 6) + (\frac{7}{12} - \frac{5}{18})\).
Use the common denominator \(216\): \(\frac{7}{12}=\frac{126}{216}\) and \(\frac{5}{18}=\frac{60}{216}\).
Compute the whole-number part: \(18-6=12\).
Compute the fraction part: \(\frac{126}{216} - \frac{60}{216}=\frac{66}{216}\), which simplifies to \(\frac{11}{36}\).
Combine the parts: \(12\frac{11}{36}\).

10) \(20\frac{11}{15} - 13\frac{7}{10} = \color{red}{7\frac{1}{30}}\)

GCF(5,150) = 5

Solution:
Separate the whole-number and fraction parts: \((20 - 13) + (\frac{11}{15} - \frac{7}{10})\).
Use the common denominator \(150\): \(\frac{11}{15}=\frac{110}{150}\) and \(\frac{7}{10}=\frac{105}{150}\).
Compute the whole-number part: \(20-13=7\).
Compute the fraction part: \(\frac{110}{150} - \frac{105}{150}=\frac{5}{150}\), which simplifies to \(\frac{1}{30}\).
Combine the parts: \(7\frac{1}{30}\).

11) \(24\frac{5}{16} - 8\frac{11}{24} = \color{red}{15\frac{41}{48}}\)

GCF(328,384) = 8

Solution:
Separate the whole-number and fraction parts: \((24 - 8) + (\frac{5}{16} - \frac{11}{24})\).
Use the common denominator \(384\): \(\frac{5}{16}=\frac{120}{384}\) and \(\frac{11}{24}=\frac{176}{384}\). Since \(\frac{120}{384}\) is smaller than \(\frac{176}{384}\), borrow \(1\) from \(24\) so the first fraction becomes \(\frac{504}{384}\).
Compute the whole-number part: \(24-1-8=15\).
Compute the fraction part: \(\frac{504}{384} - \frac{176}{384}=\frac{328}{384}\), which simplifies to \(\frac{41}{48}\).
Combine the parts: \(15\frac{41}{48}\).

12) \(30\frac{13}{20} - 19\frac{7}{12} = \color{red}{11\frac{1}{15}}\)

GCF(16,240) = 16

Solution:
Separate the whole-number and fraction parts: \((30 - 19) + (\frac{13}{20} - \frac{7}{12})\).
Use the common denominator \(240\): \(\frac{13}{20}=\frac{156}{240}\) and \(\frac{7}{12}=\frac{140}{240}\).
Compute the whole-number part: \(30-19=11\).
Compute the fraction part: \(\frac{156}{240} - \frac{140}{240}=\frac{16}{240}\), which simplifies to \(\frac{1}{15}\).
Combine the parts: \(11\frac{1}{15}\).

13) \(35\frac{17}{21} - 16\frac{19}{28} = \color{red}{19\frac{11}{84}}\)

GCF(77,588) = 7

Solution:
Separate the whole-number and fraction parts: \((35 - 16) + (\frac{17}{21} - \frac{19}{28})\).
Use the common denominator \(588\): \(\frac{17}{21}=\frac{476}{588}\) and \(\frac{19}{28}=\frac{399}{588}\).
Compute the whole-number part: \(35-16=19\).
Compute the fraction part: \(\frac{476}{588} - \frac{399}{588}=\frac{77}{588}\), which simplifies to \(\frac{11}{84}\).
Combine the parts: \(19\frac{11}{84}\).

14) \(42\frac{23}{30} - 27\frac{17}{20} = \color{red}{14\frac{11}{12}}\)

GCF(550,600) = 50

Solution:
Separate the whole-number and fraction parts: \((42 - 27) + (\frac{23}{30} - \frac{17}{20})\).
Use the common denominator \(600\): \(\frac{23}{30}=\frac{460}{600}\) and \(\frac{17}{20}=\frac{510}{600}\). Since \(\frac{460}{600}\) is smaller than \(\frac{510}{600}\), borrow \(1\) from \(42\) so the first fraction becomes \(\frac{1060}{600}\).
Compute the whole-number part: \(42-1-27=14\).
Compute the fraction part: \(\frac{1060}{600} - \frac{510}{600}=\frac{550}{600}\), which simplifies to \(\frac{11}{12}\).
Combine the parts: \(14\frac{11}{12}\).

15) \(50\frac{29}{36} - 31\frac{13}{18} = \color{red}{19\frac{1}{12}}\)

GCF(54,648) = 54

Solution:
Separate the whole-number and fraction parts: \((50 - 31) + (\frac{29}{36} - \frac{13}{18})\).
Use the common denominator \(648\): \(\frac{29}{36}=\frac{522}{648}\) and \(\frac{13}{18}=\frac{468}{648}\).
Compute the whole-number part: \(50-31=19\).
Compute the fraction part: \(\frac{522}{648} - \frac{468}{648}=\frac{54}{648}\), which simplifies to \(\frac{1}{12}\).
Combine the parts: \(19\frac{1}{12}\).

16) \(61\frac{31}{40} - 28\frac{17}{32} = \color{red}{33\frac{39}{160}}\)

GCF(312,1280) = 8

Solution:
Separate the whole-number and fraction parts: \((61 - 28) + (\frac{31}{40} - \frac{17}{32})\).
Use the common denominator \(1280\): \(\frac{31}{40}=\frac{992}{1280}\) and \(\frac{17}{32}=\frac{680}{1280}\).
Compute the whole-number part: \(61-28=33\).
Compute the fraction part: \(\frac{992}{1280} - \frac{680}{1280}=\frac{312}{1280}\), which simplifies to \(\frac{39}{160}\).
Combine the parts: \(33\frac{39}{160}\).

17) \(75\frac{37}{45} - 44\frac{29}{60} = \color{red}{31\frac{61}{180}}\)

GCF(915,2700) = 15

Solution:
Separate the whole-number and fraction parts: \((75 - 44) + (\frac{37}{45} - \frac{29}{60})\).
Use the common denominator \(2700\): \(\frac{37}{45}=\frac{2220}{2700}\) and \(\frac{29}{60}=\frac{1305}{2700}\).
Compute the whole-number part: \(75-44=31\).
Compute the fraction part: \(\frac{2220}{2700} - \frac{1305}{2700}=\frac{915}{2700}\), which simplifies to \(\frac{61}{180}\).
Combine the parts: \(31\frac{61}{180}\).

18) \(90\frac{41}{56} - 58\frac{33}{70} = \color{red}{32\frac{73}{280}}\)

GCF(1022,3920) = 14

Solution:
Separate the whole-number and fraction parts: \((90 - 58) + (\frac{41}{56} - \frac{33}{70})\).
Use the common denominator \(3920\): \(\frac{41}{56}=\frac{2870}{3920}\) and \(\frac{33}{70}=\frac{1848}{3920}\).
Compute the whole-number part: \(90-58=32\).
Compute the fraction part: \(\frac{2870}{3920} - \frac{1848}{3920}=\frac{1022}{3920}\), which simplifies to \(\frac{73}{280}\).
Combine the parts: \(32\frac{73}{280}\).

19) \(125\frac{47}{72} - 88\frac{55}{96} = \color{red}{37\frac{23}{288}}\)

GCF(552,6912) = 24

Solution:
Separate the whole-number and fraction parts: \((125 - 88) + (\frac{47}{72} - \frac{55}{96})\).
Use the common denominator \(6912\): \(\frac{47}{72}=\frac{4512}{6912}\) and \(\frac{55}{96}=\frac{3960}{6912}\).
Compute the whole-number part: \(125-88=37\).
Compute the fraction part: \(\frac{4512}{6912} - \frac{3960}{6912}=\frac{552}{6912}\), which simplifies to \(\frac{23}{288}\).
Combine the parts: \(37\frac{23}{288}\).

20) \(150\frac{59}{84} - 97\frac{65}{112} = \color{red}{53\frac{41}{336}}\)

GCF(1148,9408) = 28

Solution:
Separate the whole-number and fraction parts: \((150 - 97) + (\frac{59}{84} - \frac{65}{112})\).
Use the common denominator \(9408\): \(\frac{59}{84}=\frac{6608}{9408}\) and \(\frac{65}{112}=\frac{5460}{9408}\).
Compute the whole-number part: \(150-97=53\).
Compute the fraction part: \(\frac{6608}{9408} - \frac{5460}{9408}=\frac{1148}{9408}\), which simplifies to \(\frac{41}{336}\).
Combine the parts: \(53\frac{41}{336}\).

How to Subtract Mixed Numbers