Adding and Subtracting Mixed Numbers with Unlike Denominators ... - Free Printable

Let's solve each of the problems step by step. The goal is to add or subtract mixed fractions and express the answers in lowest terms.

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General Steps:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator if needed.
3. Add or subtract the fractions.
4. Simplify the result and convert back to a mixed number if necessary.
5. Reduce to lowest terms.

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Let’s go through each problem:

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1. $ 2\frac{1}{5} + 1\frac{3}{4} $

Convert to improper fractions:
- $ 2\frac{1}{5} = \frac{11}{5} $
- $ 1\frac{3}{4} = \frac{7}{4} $

Find LCD of 5 and 4 → 20

Convert:
- $ \frac{11}{5} = \frac{44}{20} $
- $ \frac{7}{4} = \frac{35}{20} $

Add:
$ \frac{44}{20} + \frac{35}{20} = \frac{79}{20} $

Convert to mixed number:
$ \frac{79}{20} = 3\frac{19}{20} $

✔ Answer: $ 3\frac{19}{20} $

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2. $ 3\frac{1}{2} - 2\frac{2}{3} $

Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 2\frac{2}{3} = \frac{8}{3} $

LCD of 2 and 3 → 6

Convert:
- $ \frac{7}{2} = \frac{21}{6} $
- $ \frac{8}{3} = \frac{16}{6} $

Subtract:
$ \frac{21}{6} - \frac{16}{6} = \frac{5}{6} $

✔ Answer: $ \frac{5}{6} $

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3. $ 3\frac{1}{2} - 3\frac{1}{2} $

Same numbers → difference is zero.

✔ Answer: $ 0 $

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4. $ 5\frac{3}{4} - 5\frac{1}{4} $

Subtract whole parts: $ 5 - 5 = 0 $
Subtract fractions: $ \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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5. $ 1\frac{1}{2} + 2\frac{3}{5} $

Convert:
- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 2\frac{3}{5} = \frac{13}{5} $

LCD of 2 and 5 → 10

Convert:
- $ \frac{3}{2} = \frac{15}{10} $
- $ \frac{13}{5} = \frac{26}{10} $

Add:
$ \frac{15}{10} + \frac{26}{10} = \frac{41}{10} $

Convert: $ \frac{41}{10} = 4\frac{1}{10} $

✔ Answer: $ 4\frac{1}{10} $

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6. $ 3\frac{1}{2} - 2\frac{5}{9} $

Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 2\frac{5}{9} = \frac{23}{9} $

LCD of 2 and 9 → 18

Convert:
- $ \frac{7}{2} = \frac{63}{18} $
- $ \frac{23}{9} = \frac{46}{18} $

Subtract:
$ \frac{63}{18} - \frac{46}{18} = \frac{17}{18} $

✔ Answer: $ \frac{17}{18} $

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7. $ 2\frac{3}{4} + 1\frac{1}{5} $

Convert:
- $ 2\frac{3}{4} = \frac{11}{4} $
- $ 1\frac{1}{5} = \frac{6}{5} $

LCD of 4 and 5 → 20

Convert:
- $ \frac{11}{4} = \frac{55}{20} $
- $ \frac{6}{5} = \frac{24}{20} $

Add:
$ \frac{55}{20} + \frac{24}{20} = \frac{79}{20} $

Convert: $ \frac{79}{20} = 3\frac{19}{20} $

✔ Answer: $ 3\frac{19}{20} $

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8. $ 3\frac{1}{4} - 2\frac{3}{8} $

Convert:
- $ 3\frac{1}{4} = \frac{13}{4} $
- $ 2\frac{3}{8} = \frac{19}{8} $

LCD of 4 and 8 → 8

Convert:
- $ \frac{13}{4} = \frac{26}{8} $
- $ \frac{19}{8} = \frac{19}{8} $

Subtract:
$ \frac{26}{8} - \frac{19}{8} = \frac{7}{8} $

✔ Answer: $ \frac{7}{8} $

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9. $ 3\frac{1}{2} - 1\frac{1}{2} $

Whole parts: $ 3 - 1 = 2 $
Fractions: $ \frac{1}{2} - \frac{1}{2} = 0 $

✔ Answer: $ 2 $

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10. $ 5\frac{1}{2} + 5\frac{1}{4} $

Convert:
- $ 5\frac{1}{2} = \frac{11}{2} $
- $ 5\frac{1}{4} = \frac{21}{4} $

LCD of 2 and 4 → 4

Convert:
- $ \frac{11}{2} = \frac{22}{4} $
- $ \frac{21}{4} = \frac{21}{4} $

Add:
$ \frac{22}{4} + \frac{21}{4} = \frac{43}{4} $

Convert: $ \frac{43}{4} = 10\frac{3}{4} $

✔ Answer: $ 10\frac{3}{4} $

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11. $ 1\frac{10}{11} - 1\frac{1}{3} $

Convert:
- $ 1\frac{10}{11} = \frac{21}{11} $
- $ 1\frac{1}{3} = \frac{4}{3} $

LCD of 11 and 3 → 33

Convert:
- $ \frac{21}{11} = \frac{63}{33} $
- $ \frac{4}{3} = \frac{44}{33} $

Subtract:
$ \frac{63}{33} - \frac{44}{33} = \frac{19}{33} $

✔ Answer: $ \frac{19}{33} $

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12. $ 1\frac{5}{12} + 3\frac{1}{3} $

Convert:
- $ 1\frac{5}{12} = \frac{17}{12} $
- $ 3\frac{1}{3} = \frac{10}{3} $

LCD of 12 and 3 → 12

Convert:
- $ \frac{10}{3} = \frac{40}{12} $

Add:
$ \frac{17}{12} + \frac{40}{12} = \frac{57}{12} $

Simplify:
$ \frac{57}{12} = \frac{19}{4} $ (divide numerator and denominator by 3)

Convert: $ \frac{19}{4} = 4\frac{3}{4} $

✔ Answer: $ 4\frac{3}{4} $

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✔ Final Answers:

1. $ 3\frac{19}{20} $
2. $ \frac{5}{6} $
3. $ 0 $
4. $ \frac{1}{2} $
5. $ 4\frac{1}{10} $
6. $ \frac{17}{18} $
7. $ 3\frac{19}{20} $
8. $ \frac{7}{8} $
9. $ 2 $
10. $ 10\frac{3}{4} $
11. $ \frac{19}{33} $
12. $ 4\frac{3}{4} $

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