Adding and Subtracting Fractions Worksheet | Printable Maths ... - Free Printable

Let's solve each problem step-by-step, following the instructions: add or subtract fractions, simplify answers, and convert to mixed numbers where possible.

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✔ Section A: Add and Subtract Unit Fractions

These are fractions with numerator 1. We need to find a common denominator.

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#### 1) $\frac{1}{8} + \frac{1}{2}$
LCM of 8 and 2 is 8.
$\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$
✔ Answer: $\boxed{\frac{5}{8}}$

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#### 2) $\frac{1}{20} + \frac{1}{5}$
LCM of 20 and 5 is 20.
$\frac{1}{20} + \frac{4}{20} = \frac{5}{20} = \frac{1}{4}$
✔ Answer: $\boxed{\frac{1}{4}}$

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#### 3) $\frac{1}{7} - \frac{1}{14}$
LCM of 7 and 14 is 14.
$\frac{2}{14} - \frac{1}{14} = \frac{1}{14}$
✔ Answer: $\boxed{\frac{1}{14}}$

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#### 4) $\frac{1}{5} - \frac{1}{15}$
LCM of 5 and 15 is 15.
$\frac{3}{15} - \frac{1}{15} = \frac{2}{15}$
✔ Answer: $\boxed{\frac{2}{15}}$

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#### 5) $\frac{1}{40} + \frac{1}{2}$
LCM of 40 and 2 is 40.
$\frac{1}{40} + \frac{20}{40} = \frac{21}{40}$
✔ Answer: $\boxed{\frac{21}{40}}$

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#### 6) $\frac{1}{2} - \frac{1}{3}$
LCM of 2 and 3 is 6.
$\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$
✔ Answer: $\boxed{\frac{1}{6}}$

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#### 7) $\frac{1}{5} + \frac{1}{4}$
LCM of 5 and 4 is 20.
$\frac{4}{20} + \frac{5}{20} = \frac{9}{20}$
✔ Answer: $\boxed{\frac{9}{20}}$

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#### 8) $\frac{1}{7} - \frac{1}{11}$
LCM of 7 and 11 is 77.
$\frac{11}{77} - \frac{7}{77} = \frac{4}{77}$
✔ Answer: $\boxed{\frac{4}{77}}$

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#### 9) $\frac{1}{15} + \frac{1}{2}$
LCM of 15 and 2 is 30.
$\frac{2}{30} + \frac{15}{30} = \frac{17}{30}$
✔ Answer: $\boxed{\frac{17}{30}}$

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#### 10) $\frac{1}{12} + \frac{1}{5}$
LCM of 12 and 5 is 60.
$\frac{5}{60} + \frac{12}{60} = \frac{17}{60}$
✔ Answer: $\boxed{\frac{17}{60}}$

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#### 11) $\frac{1}{5} + \frac{1}{8}$
LCM of 5 and 8 is 40.
$\frac{8}{40} + \frac{5}{40} = \frac{13}{40}$
✔ Answer: $\boxed{\frac{13}{40}}$

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#### 12) $\frac{1}{9} - \frac{1}{10}$
LCM of 9 and 10 is 90.
$\frac{10}{90} - \frac{9}{90} = \frac{1}{90}$
✔ Answer: $\boxed{\frac{1}{90}}$

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✔ Section B: Add and Subtract Fractions (Not Unit)

Now we work with non-unit fractions.

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#### 1) $\frac{1}{15} + \frac{2}{5}$
Convert $\frac{2}{5} = \frac{6}{15}$
$\frac{1}{15} + \frac{6}{15} = \frac{7}{15}$
✔ Answer: $\boxed{\frac{7}{15}}$

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#### 2) $\frac{2}{3} - \frac{1}{21}$
LCM of 3 and 21 is 21.
$\frac{14}{21} - \frac{1}{21} = \frac{13}{21}$
✔ Answer: $\boxed{\frac{13}{21}}$

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#### 3) $\frac{1}{4} + \frac{5}{12}$
LCM of 4 and 12 is 12.
$\frac{3}{12} + \frac{5}{12} = \frac{8}{12} = \frac{2}{3}$
✔ Answer: $\boxed{\frac{2}{3}}$

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#### 4) $\frac{1}{2} - \frac{7}{16}$
LCM of 2 and 16 is 16.
$\frac{8}{16} - \frac{7}{16} = \frac{1}{16}$
✔ Answer: $\boxed{\frac{1}{16}}$

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#### 5) $\frac{3}{5} + \frac{1}{2}$
LCM of 5 and 2 is 10.
$\frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10}$
✔ Answer: $\boxed{1\frac{1}{10}}$

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#### 6) $\frac{1}{6} + \frac{9}{10}$
LCM of 6 and 10 is 30.
$\frac{5}{30} + \frac{27}{30} = \frac{32}{30} = \frac{16}{15} = 1\frac{1}{15}$
✔ Answer: $\boxed{1\frac{1}{15}}$

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#### 7) $\frac{3}{7} - \frac{2}{5}$
LCM of 7 and 5 is 35.
$\frac{15}{35} - \frac{14}{35} = \frac{1}{35}$
✔ Answer: $\boxed{\frac{1}{35}}$

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#### 8) $\frac{7}{11} + \frac{2}{3}$
LCM of 11 and 3 is 33.
$\frac{21}{33} + \frac{22}{33} = \frac{43}{33} = 1\frac{10}{33}$
✔ Answer: $\boxed{1\frac{10}{33}}$

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#### 9) $\frac{4}{5} - \frac{5}{8}$
LCM of 5 and 8 is 40.
$\frac{32}{40} - \frac{25}{40} = \frac{7}{40}$
✔ Answer: $\boxed{\frac{7}{40}}$

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#### 10) $\frac{3}{10} + \frac{6}{7}$
LCM of 10 and 7 is 70.
$\frac{21}{70} + \frac{60}{70} = \frac{81}{70} = 1\frac{11}{70}$
✔ Answer: $\boxed{1\frac{11}{70}}$

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#### 11) $\frac{7}{9} + \frac{3}{8}$
LCM of 9 and 8 is 72.
$\frac{56}{72} + \frac{27}{72} = \frac{83}{72} = 1\frac{11}{72}$
✔ Answer: $\boxed{1\frac{11}{72}}$

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#### 12) $\frac{3}{4} - \frac{6}{15}$
Simplify $\frac{6}{15} = \frac{2}{5}$
Now: $\frac{3}{4} - \frac{2}{5}$
LCM of 4 and 5 is 20.
$\frac{15}{20} - \frac{8}{20} = \frac{7}{20}$
✔ Answer: $\boxed{\frac{7}{20}}$

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✔ Section C: Mixed Numbers and Improper Fractions

We’ll convert to improper fractions when needed, then simplify.

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#### 1) $3 + \frac{56}{9}$
$3 = \frac{27}{9}$, so:
$\frac{27}{9} + \frac{56}{9} = \frac{83}{9} = 9\frac{2}{9}$
✔ Answer: $\boxed{9\frac{2}{9}}$

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#### 2) $7\frac{2}{3} + 5$
$7\frac{2}{3} = \frac{23}{3}$, $5 = \frac{15}{3}$
$\frac{23}{3} + \frac{15}{3} = \frac{38}{3} = 12\frac{2}{3}$
✔ Answer: $\boxed{12\frac{2}{3}}$

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#### 3) $1\frac{1}{3} + 2\frac{1}{5}$
Convert:
$1\frac{1}{3} = \frac{4}{3}$, $2\frac{1}{5} = \frac{11}{5}$
LCM of 3 and 5 is 15.
$\frac{20}{15} + \frac{33}{15} = \frac{53}{15} = 3\frac{8}{15}$
✔ Answer: $\boxed{3\frac{8}{15}}$

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#### 4) $2\frac{1}{4} + 3\frac{1}{2}$
Convert:
$2\frac{1}{4} = \frac{9}{4}$, $3\frac{1}{2} = \frac{7}{2}$
LCM of 4 and 2 is 4.
$\frac{9}{4} + \frac{14}{4} = \frac{23}{4} = 5\frac{3}{4}$
✔ Answer: $\boxed{5\frac{3}{4}}$

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#### 5) $8\frac{1}{3} + 4\frac{2}{5}$
Convert:
$8\frac{1}{3} = \frac{25}{3}$, $4\frac{2}{5} = \frac{22}{5}$
LCM of 3 and 5 is 15.
$\frac{125}{15} + \frac{66}{15} = \frac{191}{15} = 12\frac{11}{15}$
✔ Answer: $\boxed{12\frac{11}{15}}$

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#### 6) $5\frac{8}{11} + 3\frac{7}{9}$
Convert:
$5\frac{8}{11} = \frac{63}{11}$, $3\frac{7}{9} = \frac{34}{9}$
LCM of 11 and 9 is 99.
$\frac{567}{99} + \frac{374}{99} = \frac{941}{99} = 9\frac{50}{99}$
✔ Answer: $\boxed{9\frac{50}{99}}$

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#### 7) $\frac{17}{8} - 1$
$1 = \frac{8}{8}$
$\frac{17}{8} - \frac{8}{8} = \frac{9}{8} = 1\frac{1}{8}$
✔ Answer: $\boxed{1\frac{1}{8}}$

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#### 8) $\frac{21}{9} - 2$
Simplify $\frac{21}{9} = \frac{7}{3}$, $2 = \frac{6}{3}$
$\frac{7}{3} - \frac{6}{3} = \frac{1}{3}$
✔ Answer: $\boxed{\frac{1}{3}}$

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#### 9) $5 - 2\frac{3}{5}$
$2\frac{3}{5} = \frac{13}{5}$, $5 = \frac{25}{5}$
$\frac{25}{5} - \frac{13}{5} = \frac{12}{5} = 2\frac{2}{5}$
✔ Answer: $\boxed{2\frac{2}{5}}$

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#### 10) $3\frac{1}{10} - 1\frac{2}{3}$
Convert:
$3\frac{1}{10} = \frac{31}{10}$, $1\frac{2}{3} = \frac{5}{3}$
LCM of 10 and 3 is 30.
$\frac{93}{30} - \frac{50}{30} = \frac{43}{30} = 1\frac{13}{30}$
✔ Answer: $\boxed{1\frac{13}{30}}$

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#### 11) $9\frac{5}{8} - 4\frac{6}{7}$
Convert:
$9\frac{5}{8} = \frac{77}{8}$, $4\frac{6}{7} = \frac{34}{7}$
LCM of 8 and 7 is 56.
$\frac{539}{56} - \frac{272}{56} = \frac{267}{56} = 4\frac{43}{56}$
✔ Answer: $\boxed{4\frac{43}{56}}$

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#### 12) $4\frac{2}{11} - 2\frac{8}{9}$
Convert:
$4\frac{2}{11} = \frac{46}{11}$, $2\frac{8}{9} = \frac{26}{9}$
LCM of 11 and 9 is 99.
$\frac{414}{99} - \frac{286}{99} = \frac{128}{99} = 1\frac{29}{99}$
✔ Answer: $\boxed{1\frac{29}{99}}$

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✔ Final Summary of Answers:

#### Section A
1. $\frac{5}{8}$
2. $\frac{1}{4}$
3. $\frac{1}{14}$
4. $\frac{2}{15}$
5. $\frac{21}{40}$
6. $\frac{1}{6}$
7. $\frac{9}{20}$
8. $\frac{4}{77}$
9. $\frac{17}{30}$
10. $\frac{17}{60}$
11. $\frac{13}{40}$
12. $\frac{1}{90}$

#### Section B
1. $\frac{7}{15}$
2. $\frac{13}{21}$
3. $\frac{2}{3}$
4. $\frac{1}{16}$
5. $1\frac{1}{10}$
6. $1\frac{1}{15}$
7. $\frac{1}{35}$
8. $1\frac{10}{33}$
9. $\frac{7}{40}$
10. $1\frac{11}{70}$
11. $1\frac{11}{72}$
12. $\frac{7}{20}$

#### Section C
1. $9\frac{2}{9}$
2. $12\frac{2}{3}$
3. $3\frac{8}{15}$
4. $5\frac{3}{4}$
5. $12\frac{11}{15}$
6. $9\frac{50}{99}$
7. $1\frac{1}{8}$
8. $\frac{1}{3}$
9. $2\frac{2}{5}$
10. $1\frac{13}{30}$
11. $4\frac{43}{56}$
12. $1\frac{29}{99}$

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