To solve these problems, we need to remember the rule for dividing fractions:
"Keep, Change, Flip."
1.
Keep the first fraction exactly as it is.
2.
Change the division sign ($\div$) to a multiplication sign ($\times$).
3.
Flip the second fraction (find its reciprocal).
Let's work through each problem step-by-step:
i. $\frac{3}{4} \div \frac{2}{4}$
* Keep $\frac{3}{4}$.
* Change $\div$ to $\times$.
* Flip $\frac{2}{4}$ to become $\frac{4}{2}$.
* Multiply: $\frac{3}{4} \times \frac{4}{2} = \frac{12}{8}$.
* Simplify: Both 12 and 8 can be divided by 4. $\frac{12 \div 4}{8 \div 4} = \frac{3}{2}$.
ii. $\frac{5}{6} \div \frac{1}{7}$
* Keep $\frac{5}{6}$.
* Change $\div$ to $\times$.
* Flip $\frac{1}{7}$ to become $\frac{7}{1}$.
* Multiply: $\frac{5}{6} \times \frac{7}{1} = \frac{35}{6}$.
iii. $\frac{1}{7} \div \frac{5}{8}$
* Keep $\frac{1}{7}$.
* Change $\div$ to $\times$.
* Flip $\frac{5}{8}$ to become $\frac{8}{5}$.
* Multiply: $\frac{1}{7} \times \frac{8}{5} = \frac{8}{35}$.
iv. $\frac{5}{6} \div \frac{1}{5}$
* Keep $\frac{5}{6}$.
* Change $\div$ to $\times$.
* Flip $\frac{1}{5}$ to become $\frac{5}{1}$.
* Multiply: $\frac{5}{6} \times \frac{5}{1} = \frac{25}{6}$.
v. $\frac{1}{7} \div \frac{2}{3}$
* Keep $\frac{1}{7}$.
* Change $\div$ to $\times$.
* Flip $\frac{2}{3}$ to become $\frac{3}{2}$.
* Multiply: $\frac{1}{7} \times \frac{3}{2} = \frac{3}{14}$.
vi. $\frac{1}{6} \div \frac{1}{8}$
* Keep $\frac{1}{6}$.
* Change $\div$ to $\times$.
* Flip $\frac{1}{8}$ to become $\frac{8}{1}$.
* Multiply: $\frac{1}{6} \times \frac{8}{1} = \frac{8}{6}$.
* Simplify: Both 8 and 6 can be divided by 2. $\frac{8 \div 2}{6 \div 2} = \frac{4}{3}$.
vii. $\frac{2}{7} \div \frac{1}{9}$
* Keep $\frac{2}{7}$.
* Change $\div$ to $\times$.
* Flip $\frac{1}{9}$ to become $\frac{9}{1}$.
* Multiply: $\frac{2}{7} \times \frac{9}{1} = \frac{18}{7}$.
viii. $\frac{1}{6} \div \frac{4}{9}$
* Keep $\frac{1}{6}$.
* Change $\div$ to $\times$.
* Flip $\frac{4}{9}$ to become $\frac{9}{4}$.
* Multiply: $\frac{1}{6} \times \frac{9}{4} = \frac{9}{24}$.
* Simplify: Both 9 and 24 can be divided by 3. $\frac{9 \div 3}{24 \div 3} = \frac{3}{8}$.
Final Answer:
i. $\frac{3}{2}$
ii. $\frac{35}{6}$
iii. $\frac{8}{35}$
iv. $\frac{25}{6}$
v. $\frac{3}{14}$
vi. $\frac{4}{3}$
vii. $\frac{18}{7}$
viii. $\frac{3}{8}$
Parent Tip: Review the logic above to help your child master the concept of divide fractions worksheet.
