Subtracting Mixed Numbers Worksheets - 15 Worksheets Library - Free Printable

To solve the problems involving subtracting mixed numbers with unlike denominators, we need to follow these steps:

Steps to Subtract Mixed Numbers:

1. Convert Mixed Numbers to Improper Fractions (if necessary).
2. Find a Common Denominator for the fractions.
3. Adjust the Numerators based on the common denominator.
4. Subtract the Fractions.
5. Simplify the Result (convert back to a mixed number if needed).

Let's solve each problem step by step.

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Problem 1: \( 3 \frac{1}{3} - 1 \frac{1}{2} \)

#### Step 1: Convert to Improper Fractions
- \( 3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{10}{3} \)
- \( 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2} \)

#### Step 2: Find a Common Denominator
The denominators are 3 and 2. The least common denominator (LCD) is 6.

#### Step 3: Adjust the Numerators
- \( \frac{10}{3} = \frac{10 \times 2}{3 \times 2} = \frac{20}{6} \)
- \( \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \)

#### Step 4: Subtract the Fractions
\[ \frac{20}{6} - \frac{9}{6} = \frac{20 - 9}{6} = \frac{11}{6} \]

#### Step 5: Simplify the Result
Convert \( \frac{11}{6} \) back to a mixed number:
\[ \frac{11}{6} = 1 \frac{5}{6} \]

Answer: \( 1 \frac{5}{6} \)

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Problem 2: \( 4 \frac{3}{5} - 2 \frac{1}{3} \)

#### Step 1: Convert to Improper Fractions
- \( 4 \frac{3}{5} = \frac{(4 \times 5) + 3}{5} = \frac{23}{5} \)
- \( 2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3} \)

#### Step 2: Find a Common Denominator
The denominators are 5 and 3. The LCD is 15.

#### Step 3: Adjust the Numerators
- \( \frac{23}{5} = \frac{23 \times 3}{5 \times 3} = \frac{69}{15} \)
- \( \frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \)

#### Step 4: Subtract the Fractions
\[ \frac{69}{15} - \frac{35}{15} = \frac{69 - 35}{15} = \frac{34}{15} \]

#### Step 5: Simplify the Result
Convert \( \frac{34}{15} \) back to a mixed number:
\[ \frac{34}{15} = 2 \frac{4}{15} \]

Answer: \( 2 \frac{4}{15} \)

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Problem 3: \( 3 \frac{1}{2} - 2 \frac{3}{5} \)

#### Step 1: Convert to Improper Fractions
- \( 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2} \)
- \( 2 \frac{3}{5} = \frac{(2 \times 5) + 3}{5} = \frac{13}{5} \)

#### Step 2: Find a Common Denominator
The denominators are 2 and 5. The LCD is 10.

#### Step 3: Adjust the Numerators
- \( \frac{7}{2} = \frac{7 \times 5}{2 \times 5} = \frac{35}{10} \)
- \( \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} \)

#### Step 4: Subtract the Fractions
\[ \frac{35}{10} - \frac{26}{10} = \frac{35 - 26}{10} = \frac{9}{10} \]

#### Step 5: Simplify the Result
\( \frac{9}{10} \) is already in simplest form.

Answer: \( \frac{9}{10} \)

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Problem 4: \( 4 \frac{2}{3} - 1 \frac{3}{5} \)

#### Step 1: Convert to Improper Fractions
- \( 4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{14}{3} \)
- \( 1 \frac{3}{5} = \frac{(1 \times 5) + 3}{5} = \frac{8}{5} \)

#### Step 2: Find a Common Denominator
The denominators are 3 and 5. The LCD is 15.

#### Step 3: Adjust the Numerators
- \( \frac{14}{3} = \frac{14 \times 5}{3 \times 5} = \frac{70}{15} \)
- \( \frac{8}{5} = \frac{8 \times 3}{5 \times 3} = \frac{24}{15} \)

#### Step 4: Subtract the Fractions
\[ \frac{70}{15} - \frac{24}{15} = \frac{70 - 24}{15} = \frac{46}{15} \]

#### Step 5: Simplify the Result
Convert \( \frac{46}{15} \) back to a mixed number:
\[ \frac{46}{15} = 3 \frac{1}{15} \]

Answer: \( 3 \frac{1}{15} \)

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Problem 5: \( 4 \frac{1}{6} - 3 \frac{5}{8} \)

#### Step 1: Convert to Improper Fractions
- \( 4 \frac{1}{6} = \frac{(4 \times 6) + 1}{6} = \frac{25}{6} \)
- \( 3 \frac{5}{8} = \frac{(3 \times 8) + 5}{8} = \frac{29}{8} \)

#### Step 2: Find a Common Denominator
The denominators are 6 and 8. The LCD is 24.

#### Step 3: Adjust the Numerators
- \( \frac{25}{6} = \frac{25 \times 4}{6 \times 4} = \frac{100}{24} \)
- \( \frac{29}{8} = \frac{29 \times 3}{8 \times 3} = \frac{87}{24} \)

#### Step 4: Subtract the Fractions
\[ \frac{100}{24} - \frac{87}{24} = \frac{100 - 87}{24} = \frac{13}{24} \]

#### Step 5: Simplify the Result
\( \frac{13}{24} \) is already in simplest form.

Answer: \( \frac{13}{24} \)

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Final Answers:

1. \( 1 \frac{5}{6} \)
2. \( 2 \frac{4}{15} \)
3. \( \frac{9}{10} \)
4. \( 3 \frac{1}{15} \)
5. \( \frac{13}{24} \)

You can continue solving the remaining problems using the same method. If you need further assistance, feel free to ask!

Final Answer:
\[
\boxed{1 \frac{5}{6}, 2 \frac{4}{15}, \frac{9}{10}, 3 \frac{1}{15}, \frac{13}{24}}
\]