Dividing mixed numbers by fractions worksheet for Grade 5 students.

The worksheet provided involves dividing mixed numbers by fractions, where the denominators are common. Let's solve each problem step by step.

Step-by-Step Solution:

#### 1. \( \frac{6}{12} \div \frac{1}{12} \)

- Step 1: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{6}{12} \div \frac{1}{12} = \frac{6}{12} \times \frac{12}{1}
\]

- Step 2: Multiply the numerators and the denominators.
\[
\frac{6 \times 12}{12 \times 1} = \frac{72}{12}
\]

- Step 3: Simplify the fraction.
\[
\frac{72}{12} = 6
\]

- Answer: \( 6 \)

---

#### 2. \( \frac{5}{8} \div \frac{1}{8} \)

- Step 1: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{5}{8} \div \frac{1}{8} = \frac{5}{8} \times \frac{8}{1}
\]

- Step 2: Multiply the numerators and the denominators.
\[
\frac{5 \times 8}{8 \times 1} = \frac{40}{8}
\]

- Step 3: Simplify the fraction.
\[
\frac{40}{8} = 5
\]

- Answer: \( 5 \)

---

#### 3. \( 1 \frac{1}{2} \div \frac{1}{2} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
1 \frac{1}{2} = \frac{3}{2}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{3}{2} \div \frac{1}{2} = \frac{3}{2} \times \frac{2}{1}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{3 \times 2}{2 \times 1} = \frac{6}{2}
\]

- Step 4: Simplify the fraction.
\[
\frac{6}{2} = 3
\]

- Answer: \( 3 \)

---

#### 4. \( \frac{9}{10} \div \frac{4}{10} \)

- Step 1: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{9}{10} \div \frac{4}{10} = \frac{9}{10} \times \frac{10}{4}
\]

- Step 2: Multiply the numerators and the denominators.
\[
\frac{9 \times 10}{10 \times 4} = \frac{90}{40}
\]

- Step 3: Simplify the fraction.
\[
\frac{90}{40} = \frac{9}{4} = 2 \frac{1}{4}
\]

- Answer: \( 2 \frac{1}{4} \)

---

#### 5. \( 4 \frac{1}{10} \div \frac{6}{10} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
4 \frac{1}{10} = \frac{41}{10}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{41}{10} \div \frac{6}{10} = \frac{41}{10} \times \frac{10}{6}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{41 \times 10}{10 \times 6} = \frac{410}{60}
\]

- Step 4: Simplify the fraction.
\[
\frac{410}{60} = \frac{41}{6} = 6 \frac{5}{6}
\]

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

---

#### 6. \( 7 \frac{1}{6} \div \frac{5}{6} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
7 \frac{1}{6} = \frac{43}{6}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{43}{6} \div \frac{5}{6} = \frac{43}{6} \times \frac{6}{5}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{43 \times 6}{6 \times 5} = \frac{258}{30}
\]

- Step 4: Simplify the fraction.
\[
\frac{258}{30} = \frac{43}{5} = 8 \frac{3}{5}
\]

- Answer: \( 8 \frac{3}{5} \)

---

#### 7. \( 5 \frac{3}{4} \div \frac{1}{4} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
5 \frac{3}{4} = \frac{23}{4}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{23}{4} \div \frac{1}{4} = \frac{23}{4} \times \frac{4}{1}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{23 \times 4}{4 \times 1} = \frac{92}{4}
\]

- Step 4: Simplify the fraction.
\[
\frac{92}{4} = 23
\]

- Answer: \( 23 \)

---

#### 8. \( 9 \frac{3}{8} \div \frac{3}{8} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
9 \frac{3}{8} = \frac{75}{8}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{75}{8} \div \frac{3}{8} = \frac{75}{8} \times \frac{8}{3}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{75 \times 8}{8 \times 3} = \frac{600}{24}
\]

- Step 4: Simplify the fraction.
\[
\frac{600}{24} = 25
\]

- Answer: \( 25 \)

---

#### 9. \( 6 \frac{4}{12} \div \frac{4}{12} \)

- Step 1: Simplify the mixed number.
\[
6 \frac{4}{12} = 6 \frac{1}{3}
\]

- Step 2: Convert the mixed number to an improper fraction.
\[
6 \frac{1}{3} = \frac{19}{3}
\]

- Step 3: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{19}{3} \div \frac{4}{12} = \frac{19}{3} \times \frac{12}{4}
\]

- Step 4: Simplify the second fraction.
\[
\frac{12}{4} = 3
\]
So,
\[
\frac{19}{3} \times 3 = \frac{19 \times 3}{3} = 19
\]

- Answer: \( 19 \)

---

#### 10. \( 6 \frac{1}{2} \div \frac{1}{2} \)

- Step 1: Convert the mixed number to an improper fraction.
\[
6 \frac{1}{2} = \frac{13}{2}
\]

- Step 2: Rewrite the division as multiplication by the reciprocal of the divisor.
\[
\frac{13}{2} \div \frac{1}{2} = \frac{13}{2} \times \frac{2}{1}
\]

- Step 3: Multiply the numerators and the denominators.
\[
\frac{13 \times 2}{2 \times 1} = \frac{26}{2}
\]

- Step 4: Simplify the fraction.
\[
\frac{26}{2} = 13
\]

- Answer: \( 13 \)

---

Final Answers:

\[
\boxed{
\begin{array}{l}
1. \ 6 \\
2. \ 5 \\
3. \ 3 \\
4. \ 2 \frac{1}{4} \\
5. \ 6 \frac{5}{6} \\
6. \ 8 \frac{3}{5} \\
7. \ 23 \\
8. \ 25 \\
9. \ 19 \\
10. \ 13 \\
\end{array}
}
\]