Divide fraction by whole number game, worksheet, quiz, flash card - Free Printable

The image you uploaded appears to be a worksheet focused on the division of fractions. Below, I will solve each problem step by step and explain the process.

General Rule for Dividing Fractions:

To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

For example:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \cdot d}{b \cdot c}
$$

Solving Each Problem:

#### Row 1:
1. $\frac{2}{6} \div 2$
- Convert $2$ to a fraction: $2 = \frac{2}{1}$.
- Reciprocal of $\frac{2}{1}$ is $\frac{1}{2}$.
- Multiply: $\frac{2}{6} \times \frac{1}{2} = \frac{2 \cdot 1}{6 \cdot 2} = \frac{2}{12} = \frac{1}{6}$.
- Answer: $\frac{1}{6}$

2. $\frac{3}{9} \div 3$
- Convert $3$ to a fraction: $3 = \frac{3}{1}$.
- Reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$.
- Multiply: $\frac{3}{9} \times \frac{1}{3} = \frac{3 \cdot 1}{9 \cdot 3} = \frac{3}{27} = \frac{1}{9}$.
- Answer: $\frac{1}{9}$

3. $\frac{2}{8} \div 4$
- Convert $4$ to a fraction: $4 = \frac{4}{1}$.
- Reciprocal of $\frac{4}{1}$ is $\frac{1}{4}$.
- Multiply: $\frac{2}{8} \times \frac{1}{4} = \frac{2 \cdot 1}{8 \cdot 4} = \frac{2}{32} = \frac{1}{16}$.
- Answer: $\frac{1}{16}$

#### Row 2:
4. $\frac{2}{1} \div 1$
- Convert $1$ to a fraction: $1 = \frac{1}{1}$.
- Reciprocal of $\frac{1}{1}$ is $\frac{1}{1}$.
- Multiply: $\frac{2}{1} \times \frac{1}{1} = \frac{2 \cdot 1}{1 \cdot 1} = \frac{2}{1} = 2$.
- Answer: $2$

5. $\frac{5}{7} \div 5$
- Convert $5$ to a fraction: $5 = \frac{5}{1}$.
- Reciprocal of $\frac{5}{1}$ is $\frac{1}{5}$.
- Multiply: $\frac{5}{7} \times \frac{1}{5} = \frac{5 \cdot 1}{7 \cdot 5} = \frac{5}{35} = \frac{1}{7}$.
- Answer: $\frac{1}{7}$

6. $\frac{3}{8} \div 6$
- Convert $6$ to a fraction: $6 = \frac{6}{1}$.
- Reciprocal of $\frac{6}{1}$ is $\frac{1}{6}$.
- Multiply: $\frac{3}{8} \times \frac{1}{6} = \frac{3 \cdot 1}{8 \cdot 6} = \frac{3}{48} = \frac{1}{16}$.
- Answer: $\frac{1}{16}$

#### Row 3:
7. $\frac{5}{3} \div 3$
- Convert $3$ to a fraction: $3 = \frac{3}{1}$.
- Reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$.
- Multiply: $\frac{5}{3} \times \frac{1}{3} = \frac{5 \cdot 1}{3 \cdot 3} = \frac{5}{9}$.
- Answer: $\frac{5}{9}$

8. $\frac{9}{5} \div 9$
- Convert $9$ to a fraction: $9 = \frac{9}{1}$.
- Reciprocal of $\frac{9}{1}$ is $\frac{1}{9}$.
- Multiply: $\frac{9}{5} \times \frac{1}{9} = \frac{9 \cdot 1}{5 \cdot 9} = \frac{9}{45} = \frac{1}{5}$.
- Answer: $\frac{1}{5}$

9. $\frac{5}{5} \div 5$
- Convert $5$ to a fraction: $5 = \frac{5}{1}$.
- Reciprocal of $\frac{5}{1}$ is $\frac{1}{5}$.
- Multiply: $\frac{5}{5} \times \frac{1}{5} = \frac{5 \cdot 1}{5 \cdot 5} = \frac{5}{25} = \frac{1}{5}$.
- Answer: $\frac{1}{5}$

#### Row 4:
10. $\frac{1}{1} \div 1$
- Convert $1$ to a fraction: $1 = \frac{1}{1}$.
- Reciprocal of $\frac{1}{1}$ is $\frac{1}{1}$.
- Multiply: $\frac{1}{1} \times \frac{1}{1} = \frac{1 \cdot 1}{1 \cdot 1} = \frac{1}{1} = 1$.
- Answer: $1$

11. $\frac{4}{5} \div 4$
- Convert $4$ to a fraction: $4 = \frac{4}{1}$.
- Reciprocal of $\frac{4}{1}$ is $\frac{1}{4}$.
- Multiply: $\frac{4}{5} \times \frac{1}{4} = \frac{4 \cdot 1}{5 \cdot 4} = \frac{4}{20} = \frac{1}{5}$.
- Answer: $\frac{1}{5}$

12. $\frac{7}{7} \div 7$
- Convert $7$ to a fraction: $7 = \frac{7}{1}$.
- Reciprocal of $\frac{7}{1}$ is $\frac{1}{7}$.
- Multiply: $\frac{7}{7} \times \frac{1}{7} = \frac{7 \cdot 1}{7 \cdot 7} = \frac{7}{49} = \frac{1}{7}$.
- Answer: $\frac{1}{7}$

#### Row 5:
13. $\frac{3}{6} \div 2$
- Convert $2$ to a fraction: $2 = \frac{2}{1}$.
- Reciprocal of $\frac{2}{1}$ is $\frac{1}{2}$.
- Multiply: $\frac{3}{6} \times \frac{1}{2} = \frac{3 \cdot 1}{6 \cdot 2} = \frac{3}{12} = \frac{1}{4}$.
- Answer: $\frac{1}{4}$

14. $\frac{2}{8} \div 8$
- Convert $8$ to a fraction: $8 = \frac{8}{1}$.
- Reciprocal of $\frac{8}{1}$ is $\frac{1}{8}$.
- Multiply: $\frac{2}{8} \times \frac{1}{8} = \frac{2 \cdot 1}{8 \cdot 8} = \frac{2}{64} = \frac{1}{32}$.
- Answer: $\frac{1}{32}$

15. $\frac{3}{3} \div 3$
- Convert $3$ to a fraction: $3 = \frac{3}{1}$.
- Reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$.
- Multiply: $\frac{3}{3} \times \frac{1}{3} = \frac{3 \cdot 1}{3 \cdot 3} = \frac{3}{9} = \frac{1}{3}$.
- Answer: $\frac{1}{3}$

#### Row 6:
16. $\frac{2}{4} \div 4$
- Convert $4$ to a fraction: $4 = \frac{4}{1}$.
- Reciprocal of $\frac{4}{1}$ is $\frac{1}{4}$.
- Multiply: $\frac{2}{4} \times \frac{1}{4} = \frac{2 \cdot 1}{4 \cdot 4} = \frac{2}{16} = \frac{1}{8}$.
- Answer: $\frac{1}{8}$

17. $\frac{1}{7} \div 7$
- Convert $7$ to a fraction: $7 = \frac{7}{1}$.
- Reciprocal of $\frac{7}{1}$ is $\frac{1}{7}$.
- Multiply: $\frac{1}{7} \times \frac{1}{7} = \frac{1 \cdot 1}{7 \cdot 7} = \frac{1}{49}$.
- Answer: $\frac{1}{49}$

18. $\frac{3}{8} \div 3$
- Convert $3$ to a fraction: $3 = \frac{3}{1}$.
- Reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$.
- Multiply: $\frac{3}{8} \times \frac{1}{3} = \frac{3 \cdot 1}{8 \cdot 3} = \frac{3}{24} = \frac{1}{8}$.
- Answer: $\frac{1}{8}$

#### Row 7:
19. $\frac{5}{5} \div 5$
- Convert $5$ to a fraction: $5 = \frac{5}{1}$.
- Reciprocal of $\frac{5}{1}$ is $\frac{1}{5}$.
- Multiply: $\frac{5}{5} \times \frac{1}{5} = \frac{5 \cdot 1}{5 \cdot 5} = \frac{5}{25} = \frac{1}{5}$.
- Answer: $\frac{1}{5}$

20. $\frac{9}{9} \div 9$
- Convert $9$ to a fraction: $9 = \frac{9}{1}$.
- Reciprocal of $\frac{9}{1}$ is $\frac{1}{9}$.
- Multiply: $\frac{9}{9} \times \frac{1}{9} = \frac{9 \cdot 1}{9 \cdot 9} = \frac{9}{81} = \frac{1}{9}$.
- Answer: $\frac{1}{9}$

21. $\frac{3}{8} \div 3$
- Convert $3$ to a fraction: $3 = \frac{3}{1}$.
- Reciprocal of $\frac{3}{1}$ is $\frac{1}{3}$.
- Multiply: $\frac{3}{8} \times \frac{1}{3} = \frac{3 \cdot 1}{8 \cdot 3} = \frac{3}{24} = \frac{1}{8}$.
- Answer: $\frac{1}{8}$

#### Row 8:
22. $\frac{7}{7} \div 7$
- Convert $7$ to a fraction: $7 = \frac{7}{1}$.
- Reciprocal of $\frac{7}{1}$ is $\frac{1}{7}$.
- Multiply: $\frac{7}{7} \times \frac{1}{7} = \frac{7 \cdot 1}{7 \cdot 7} = \frac{7}{49} = \frac{1}{7}$.
- Answer: $\frac{1}{7}$

23. $\frac{5}{5} \div 5$
- Convert $5$ to a fraction: $5 = \frac{5}{1}$.
- Reciprocal of $\frac{5}{1}$ is $\frac{1}{5}$.
- Multiply: $\frac{5}{5} \times \frac{1}{5} = \frac{5 \cdot 1}{5 \cdot 5} = \frac{5}{25} = \frac{1}{5}$.
- Answer: $\frac{1}{5}$

24. $\frac{7}{8} \div 7$
- Convert $7$ to a fraction: $7 = \frac{7}{1}$.
- Reciprocal of $\frac{7}{1}$ is $\frac{1}{7}$.
- Multiply: $\frac{7}{8} \times \frac{1}{7} = \frac{7 \cdot 1}{8 \cdot 7} = \frac{7}{56} = \frac{1}{8}$.
- Answer: $\frac{1}{8}$

Final Answers:

$$
\boxed{
\begin{array}{ccc}
\frac{1}{6} & \frac{1}{9} & \frac{1}{16} \\
2 & \frac{1}{7} & \frac{1}{16} \\
\frac{5}{9} & \frac{1}{5} & \frac{1}{5} \\
1 & \frac{1}{5} & \frac{1}{7} \\
\frac{1}{4} & \frac{1}{32} & \frac{1}{3} \\
\frac{1}{8} & \frac{1}{49} & \frac{1}{8} \\
\frac{1}{5} & \frac{1}{9} & \frac{1}{8} \\
\frac{1}{7} & \frac{1}{5} & \frac{1}{8} \\
\end{array}
}
$$