Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

To solve these problems, we use 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 (swap the top and bottom numbers). This is called finding the reciprocal.

Then, multiply the numerators (top numbers) together and the denominators (bottom numbers) together. Finally, simplify the answer if possible.

Here are the step-by-step solutions for each problem:

1. $\frac{1}{3} \div \frac{7}{9}$
* Keep $\frac{1}{3}$, change to $\times$, flip $\frac{7}{9}$ to $\frac{9}{7}$.
* $\frac{1}{3} \times \frac{9}{7} = \frac{1 \times 9}{3 \times 7} = \frac{9}{21}$
* Simplify by dividing top and bottom by 3: $\frac{3}{7}$

2. $\frac{1}{5} \div \frac{5}{8}$
* Keep $\frac{1}{5}$, change to $\times$, flip $\frac{5}{8}$ to $\frac{8}{5}$.
* $\frac{1}{5} \times \frac{8}{5} = \frac{1 \times 8}{5 \times 5} = \frac{8}{25}$

3. $\frac{10}{11} \div \frac{20}{22}$
* Keep $\frac{10}{11}$, change to $\times$, flip $\frac{20}{22}$ to $\frac{22}{20}$.
* $\frac{10}{11} \times \frac{22}{20}$
* We can cross-cancel before multiplying: 10 goes into 20 twice, and 11 goes into 22 twice.
* $\frac{1}{1} \times \frac{2}{2} = \frac{2}{2} = 1$

4. $\frac{2}{3} \div \frac{18}{15}$
* Keep $\frac{2}{3}$, change to $\times$, flip $\frac{18}{15}$ to $\frac{15}{18}$.
* $\frac{2}{3} \times \frac{15}{18}$
* Cross-cancel: 3 goes into 15 five times. So, $\frac{2}{1} \times \frac{5}{18} = \frac{10}{18}$.
* Simplify $\frac{10}{18}$ by dividing by 2: $\frac{5}{9}$

5. $\frac{1}{9} \div \frac{3}{10}$
* Keep $\frac{1}{9}$, change to $\times$, flip $\frac{3}{10}$ to $\frac{10}{3}$.
* $\frac{1}{9} \times \frac{10}{3} = \frac{1 \times 10}{9 \times 3} = \frac{10}{27}$

6. $\frac{7}{16} \div \frac{9}{8}$
* Keep $\frac{7}{16}$, change to $\times$, flip $\frac{9}{8}$ to $\frac{8}{9}$.
* $\frac{7}{16} \times \frac{8}{9}$
* Cross-cancel: 8 goes into 16 two times. So, $\frac{7}{2} \times \frac{1}{9} = \frac{7}{18}$

7. $\frac{4}{5} \div \frac{1}{10}$
* Keep $\frac{4}{5}$, change to $\times$, flip $\frac{1}{10}$ to $\frac{10}{1}$.
* $\frac{4}{5} \times \frac{10}{1}$
* Cross-cancel: 5 goes into 10 two times. So, $\frac{4}{1} \times \frac{2}{1} = \frac{8}{1} = 8$

8. $\frac{1}{11} \div \frac{4}{44}$
* Keep $\frac{1}{11}$, change to $\times$, flip $\frac{4}{44}$ to $\frac{44}{4}$.
* $\frac{1}{11} \times \frac{44}{4}$
* Note that $\frac{44}{4} = 11$. So, $\frac{1}{11} \times 11 = \frac{11}{11} = 1$
* Alternatively: $\frac{1 \times 44}{11 \times 4} = \frac{44}{44} = 1$

9. $\frac{3}{13} \div \frac{2}{3}$
* Keep $\frac{3}{13}$, change to $\times$, flip $\frac{2}{3}$ to $\frac{3}{2}$.
* $\frac{3}{13} \times \frac{3}{2} = \frac{3 \times 3}{13 \times 2} = \frac{9}{26}$

10. $\frac{8}{25} \div \frac{16}{32}$
* Keep $\frac{8}{25}$, change to $\times$, flip $\frac{16}{32}$ to $\frac{32}{16}$.
* Note that $\frac{32}{16} = 2$. So, $\frac{8}{25} \times 2 = \frac{16}{25}$

11. $\frac{1}{7} \div \frac{3}{42}$
* Keep $\frac{1}{7}$, change to $\times$, flip $\frac{3}{42}$ to $\frac{42}{3}$.
* $\frac{1}{7} \times \frac{42}{3}$
* Cross-cancel: 7 goes into 42 six times. So, $\frac{1}{1} \times \frac{6}{3} = \frac{6}{3} = 2$

12. $\frac{8}{9} \div \frac{32}{45}$
* Keep $\frac{8}{9}$, change to $\times$, flip $\frac{32}{45}$ to $\frac{45}{32}$.
* $\frac{8}{9} \times \frac{45}{32}$
* Cross-cancel: 8 goes into 32 four times. 9 goes into 45 five times.
* $\frac{1}{1} \times \frac{5}{4} = \frac{5}{4}$ (or $1 \frac{1}{4}$)

Final Answer:
1. $\frac{3}{7}$
2. $\frac{8}{25}$
3. $1$
4. $\frac{5}{9}$
5. $\frac{10}{27}$
6. $\frac{7}{18}$
7. $8$
8. $1$
9. $\frac{9}{26}$
10. $\frac{16}{25}$
11. $2$
12. $\frac{5}{4}$