Dividing Fractions and Whole Numbers Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Dividing Mixed Numbers by Whole Numbers", and it contains several problems where mixed numbers are being divided by whole numbers.

Let me solve each problem step-by-step and explain the process.

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🔧 General Rule:

To divide a mixed number by a whole number, follow these steps:

1. Convert the mixed number to an improper fraction.
2. Write the whole number as a fraction (over 1).
3. Multiply by the reciprocal of the whole number.
4. Simplify the result and convert back to a mixed number if needed.

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Now let’s solve each problem:

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1. $ 6 \frac{3}{5} \div 11 $

Step 1: Convert $ 6 \frac{3}{5} $ to an improper fraction:
$$
6 \frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{30 + 3}{5} = \frac{33}{5}
$$

Step 2: Divide by 11:
$$
\frac{33}{5} \div 11 = \frac{33}{5} \times \frac{1}{11} = \frac{33}{55}
$$

Step 3: Simplify:
$$
\frac{33}{55} = \frac{3}{5} \quad (\text{divide numerator and denominator by } 11)
$$

✔ Answer: $ \boxed{\frac{3}{5}} $

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2. $ 4 \frac{3}{8} \div 8 $

Step 1: Convert $ 4 \frac{3}{8} $:
$$
4 \frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}
$$

Step 2: Divide by 8:
$$
\frac{35}{8} \div 8 = \frac{35}{8} \times \frac{1}{8} = \frac{35}{64}
$$

✔ Answer: $ \boxed{\frac{35}{64}} $

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

Step 1: Convert $ 5 \frac{1}{4} $:
$$
5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}
$$

Step 2: Divide by 5:
$$
\frac{21}{4} \div 5 = \frac{21}{4} \times \frac{1}{5} = \frac{21}{20}
$$

Step 3: Convert to mixed number:
$$
\frac{21}{20} = 1 \frac{1}{20}
$$

✔ Answer: $ \boxed{1 \frac{1}{20}} $

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4. $ 1 \frac{2}{3} \div 14 $

Step 1: Convert $ 1 \frac{2}{3} $:
$$
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
$$

Step 2: Divide by 14:
$$
\frac{5}{3} \div 14 = \frac{5}{3} \times \frac{1}{14} = \frac{5}{42}
$$

✔ Answer: $ \boxed{\frac{5}{42}} $

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5. $ 9 \frac{3}{4} \div 18 $

Step 1: Convert $ 9 \frac{3}{4} $:
$$
9 \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}
$$

Step 2: Divide by 18:
$$
\frac{39}{4} \div 18 = \frac{39}{4} \times \frac{1}{18} = \frac{39}{72}
$$

Step 3: Simplify:
$$
\frac{39}{72} = \frac{13}{24} \quad (\text{divide by } 3)
$$

✔ Answer: $ \boxed{\frac{13}{24}} $

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6. $ 7 \frac{1}{3} \div 3 $

Step 1: Convert $ 7 \frac{1}{3} $:
$$
7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3}
$$

Step 2: Divide by 3:
$$
\frac{22}{3} \div 3 = \frac{22}{3} \times \frac{1}{3} = \frac{22}{9}
$$

Step 3: Convert to mixed number:
$$
\frac{22}{9} = 2 \frac{4}{9}
$$

✔ Answer: $ \boxed{2 \frac{4}{9}} $

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7. $ 7 \frac{1}{4} \div 7 $

Step 1: Convert $ 7 \frac{1}{4} $:
$$
7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}
$$

Step 2: Divide by 7:
$$
\frac{29}{4} \div 7 = \frac{29}{4} \times \frac{1}{7} = \frac{29}{28}
$$

Step 3: Convert to mixed number:
$$
\frac{29}{28} = 1 \frac{1}{28}
$$

✔ Answer: $ \boxed{1 \frac{1}{28}} $

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8. $ 6 \frac{2}{3} \div 16 $

Step 1: Convert $ 6 \frac{2}{3} $:
$$
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
$$

Step 2: Divide by 16:
$$
\frac{20}{3} \div 16 = \frac{20}{3} \times \frac{1}{16} = \frac{20}{48}
$$

Step 3: Simplify:
$$
\frac{20}{48} = \frac{5}{12} \quad (\text{divide by } 4)
$$

✔ Answer: $ \boxed{\frac{5}{12}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. $ 6 \frac{3}{5} \div 11 $ | $ \frac{3}{5} $ |
| 2. $ 4 \frac{3}{8} \div 8 $ | $ \frac{35}{64} $ |
| 3. $ 5 \frac{1}{4} \div 5 $ | $ 1 \frac{1}{20} $ |
| 4. $ 1 \frac{2}{3} \div 14 $ | $ \frac{5}{42} $ |
| 5. $ 9 \frac{3}{4} \div 18 $ | $ \frac{13}{24} $ |
| 6. $ 7 \frac{1}{3} \div 3 $ | $ 2 \frac{4}{9} $ |
| 7. $ 7 \frac{1}{4} \div 7 $ | $ 1 \frac{1}{28} $ |
| 8. $ 6 \frac{2}{3} \div 16 $ | $ \frac{5}{12} $ |

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Let me know if you'd like this formatted as a printable answer sheet or want explanations in simpler terms!