# Spectrum Math Grade 6 Chapter 2 Lesson 4 Answer Key Dividing Mixed Numbers

Go through the Spectrum Math Grade 6 Answer Key Chapter 2 Lesson 2.4 Dividing Mixed Numbers and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 2 Lesson 2.4 Dividing Mixed Numbers Answers Key

3$$\frac{2}{5}$$ ÷ 4 Rename 3$$\frac{2}{5}$$ as $$\frac{17}{5}$$.
$$\frac{17}{5}$$ ÷ $$\frac{4}{1}$$ Rename 4 as $$\frac{4}{1}$$.
$$\frac{17}{5}$$ × $$\frac{1}{4}$$ = $$\frac{17}{20}$$ Multiply by the reciprocal.

4$$\frac{1}{3}$$ ÷ 2$$\frac{3}{4}$$
$$\frac{13}{3}$$ ÷ $$\frac{11}{4}$$ Rename
$$\frac{13}{3}$$ × $$\frac{4}{11}$$ = $$\frac{52}{33}$$ = 1$$\frac{19}{33}$$ Multiply by the reciprocal.

Divide. Write answers in simplest form.

Question 1.
a. 2$$\frac{1}{2}$$ ÷ 3$$\frac{1}{3}$$
Simplest form of 2$$\frac{1}{2}$$ ÷ 3$$\frac{1}{3}$$ is $$\frac{3}{4}$$.

Explanation:
2$$\frac{1}{2}$$ ÷ 3$$\frac{1}{3}$$
= 2$$\frac{1}{2}$$ ÷ 3$$\frac{1}{3}$$
= {[(2 × 2) + 1] ÷ 2} ÷ {[(3 × 3) + 1] ÷ 3}
= [(4 + 1) ÷ 2] ÷ [(9 + 1) ÷ 3]
= $$\frac{5}{2}$$ ÷ $$\frac{10}{3}$$
= $$\frac{5}{2}$$ × $$\frac{3}{10}$$
= $$\frac{1}{2}$$ × $$\frac{3}{2}$$
= $$\frac{3}{4}$$

b. 1$$\frac{1}{8}$$ ÷ 2$$\frac{1}{4}$$
Simplest form of 1$$\frac{1}{8}$$ ÷ 2$$\frac{1}{4}$$ is $$\frac{1}{2}$$.

Explanation:
1$$\frac{1}{8}$$ ÷ 2$$\frac{1}{4}$$
= {[(1 × 8) + 1] ÷ 8} ÷ {[(2 × 4) + 1] ÷ 4}
= [(8 + 1) ÷ 8] ÷ [(8 + 1) ÷ 4]
= $$\frac{9}{8}$$ ÷ $$\frac{9}{4}$$
= $$\frac{9}{8}$$ × $$\frac{4}{9}$$
= $$\frac{1}{8}$$ × $$\frac{4}{1}$$
= $$\frac{1}{2}$$ × $$\frac{1}{1}$$
= $$\frac{1}{2}$$.

c. 8 ÷ 3$$\frac{1}{2}$$
Simplest form of 8 ÷ 3$$\frac{1}{2}$$ is $$\frac{16}{7}$$ or 2$$\frac{2}{7}$$.

Explanation:
8 ÷ 3$$\frac{1}{2}$$
= 8 ÷ {[(3 × 2) + 1] ÷ 2}
= 8 ÷ [(6 + 1) ÷ 2]
= 8 ÷ $$\frac{7}{2}$$
= 8 × $$\frac{2}{7}$$
= $$\frac{16}{7}$$ or 2$$\frac{2}{7}$$

d. 2$$\frac{1}{3}$$ ÷ 5
Simplest form of 2$$\frac{1}{3}$$ ÷ 5 is $$\frac{7}{15}$$.

Explanation:
2$$\frac{1}{3}$$ ÷ 5
= {[(2 × 3) + 1] ÷ 3} ÷ 5
= [(6 + 1) ÷ 3] ÷ 5
= $$\frac{7}{3}$$ ÷ 5
= $$\frac{7}{3}$$ × $$\frac{1}{5}$$
= $$\frac{7}{15}$$

Question 2.
a. 4$$\frac{1}{2}$$ ÷ 1$$\frac{1}{6}$$
Simplest form of 4$$\frac{1}{2}$$ ÷ 1$$\frac{1}{6}$$ is $$\frac{27}{7}$$ or 3$$\frac{6}{7}$$.

Explanation:
4$$\frac{1}{2}$$ ÷ 1$$\frac{1}{6}$$
= {[(4 × 2) + 1] ÷ 2} ÷ {[(1 × 6) + 1] ÷ 6}
= [(8 + 1) ÷ 2] ÷ [(6 + 1) ÷ 6]
= $$\frac{9}{2}$$ ÷ $$\frac{7}{6}$$
= $$\frac{9}{2}$$ × $$\frac{6}{7}$$
= $$\frac{9}{1}$$ × $$\frac{3}{7}$$
= $$\frac{27}{7}$$ or 3$$\frac{6}{7}$$

b. 4$$\frac{5}{6}$$ ÷ 2$$\frac{2}{5}$$
Simplest form of 4$$\frac{5}{6}$$ ÷ 2$$\frac{2}{5}$$ is $$\frac{145}{72}$$ or 2$$\frac{1}{72}$$.

Explanation:
4$$\frac{5}{6}$$ ÷ 2$$\frac{2}{5}$$
= {[(4 × 6) + 5] ÷ 6} ÷ {[(2 × 5) + 2] ÷ 5}
= [(24 + 5) ÷ 6] ÷ [(10 + 2) ÷ 5]
= $$\frac{29}{6}$$ ÷ $$\frac{12}{5}$$
= $$\frac{29}{6}$$ × $$\frac{5}{12}$$
= $$\frac{145}{72}$$ or 2$$\frac{1}{72}$$

c. 4$$\frac{1}{3}$$ ÷ 6
Simplest form of 4$$\frac{1}{3}$$ ÷ 6 is $$\frac{13}{18}$$.

Explanation:
4$$\frac{1}{3}$$ ÷ 6
= {[(4 × 3) + 1] ÷ 3} ÷ 6
= [(12 + 1) ÷ 3] ÷ 6
= $$\frac{13}{3}$$ ÷ 6
= $$\frac{13}{3}$$ × $$\frac{1}{6}$$
= $$\frac{13}{18}$$

d. 1$$\frac{1}{2}$$ ÷ 3$$\frac{1}{8}$$
Simplest form of 1$$\frac{1}{2}$$ ÷ 3$$\frac{1}{8}$$ is $$\frac{12}{25}$$.

Explanation:
1$$\frac{1}{2}$$ ÷ 3$$\frac{1}{8}$$
= {[(1 × 2) + 1] ÷ 2} ÷ {[(3 × 8) + 1] ÷ 8}
= [(2 + 1) ÷ 2] ÷ [(24 + 1) ÷ 8]
= $$\frac{3}{2}$$ ÷ $$\frac{25}{8}$$
= $$\frac{3}{2}$$ × $$\frac{8}{25}$$
= $$\frac{3}{1}$$ × $$\frac{4}{25}$$
= $$\frac{12}{25}$$

Question 3.
a. 6 ÷ 2$$\frac{1}{2}$$
Simplest form of 6 ÷ 2$$\frac{1}{2}$$ is $$\frac{12}{5}$$ or 2$$\frac{2}{5}$$.

Explanation:
6 ÷ 2$$\frac{1}{2}$$
= 6÷ {[(2 × 2) + 1] ÷ 2}
= 6 ÷ [(4 + 1) ÷ 2]
= 6 ÷ $$\frac{5}{2}$$
= 6 × $$\frac{2}{5}$$
= $$\frac{12}{5}$$ or 2$$\frac{2}{5}$$

b. 1$$\frac{1}{2}$$ ÷ 3
Simplest form of 1$$\frac{1}{2}$$ ÷ 3 is $$\frac{1}{2}$$.

Explanation:
1$$\frac{1}{2}$$ ÷ 3
= {[(1 × 2) + 1] ÷ 2} ÷ 3
= [(2 + 1) ÷ 2] ÷ 3
= $$\frac{3}{2}$$ ÷ 3
= $$\frac{3}{2}$$ × $$\frac{1}{3}$$
= $$\frac{1}{2}$$ × $$\frac{1}{1}$$
= $$\frac{1}{2}$$

c. 5 ÷ 3$$\frac{3}{4}$$
Simplest form of 5 ÷ 3$$\frac{3}{4}$$ is $$\frac{4}{3}$$ or 1$$\frac{1}{3}$$.

Explanation:
5 ÷ 3$$\frac{3}{4}$$
= 5 ÷ {[(3 × 4) + 3] ÷ 4}
= 5 ÷ [(12 + 3) ÷ 4]
= 5 ÷ $$\frac{15}{4}$$
= 5 × $$\frac{4}{15}$$
= 1 × $$\frac{4}{3}$$
= $$\frac{4}{3}$$ or 1$$\frac{1}{3}$$

d. 2$$\frac{1}{8}$$ ÷ 3
Simplest form of 2$$\frac{1}{8}$$ ÷ 3 is $$\frac{17}{24}$$.

Explanation:
2$$\frac{1}{8}$$ ÷ 3
= {[(2 × 8) + 1] ÷ 8} ÷ 3
= [(16 + 1) ÷ 8] ÷ 3
= $$\frac{17}{8}$$ ÷ 3
= $$\frac{17}{8}$$ × $$\frac{1}{3}$$
= $$\frac{17}{24}$$

Question 4.
a.
3$$\frac{3}{5}$$ ÷ 4
Simplest form of 3$$\frac{3}{5}$$ ÷ 4 is $$\frac{9}{10}$$.

Explanation:
3$$\frac{3}{5}$$ ÷ 4
= {[(3 × 5) + 3] ÷ 5} ÷ 4
= [(15 + 3) ÷ 5] ÷ 4
= $$\frac{18}{5}$$ ÷ 4
= $$\frac{18}{5}$$ × $$\frac{1}{4}$$
= $$\frac{18}{5}$$ × $$\frac{1}{4}$$
= $$\frac{9}{5}$$ × $$\frac{1}{2}$$
= $$\frac{9}{10}$$

b. 3$$\frac{1}{3}$$ ÷ 2$$\frac{3}{8}$$
Simplest form of 3$$\frac{1}{3}$$ ÷ 2$$\frac{3}{8}$$ is $$\frac{80}{57}$$ or 1$$\frac{23}{57}$$.

Explanation:
3$$\frac{1}{3}$$ ÷ 2$$\frac{3}{8}$$
= {[(3 × 3) + 1] ÷ 3} ÷ {[(2 × 8) + 3] ÷ 8}
= [(9 + 1) ÷ 3] ÷ [(16 + 3) ÷ 8]
= $$\frac{10}{3}$$ ÷ $$\frac{19}{8}$$
= $$\frac{10}{3}$$ × $$\frac{8}{19}$$
= $$\frac{80}{57}$$ or 1$$\frac{23}{57}$$

c. 1 ÷ 4$$\frac{1}{3}$$
Simplest form of 1 ÷ 4$$\frac{1}{3}$$ is $$\frac{3}{13}$$.

Explanation:
1 ÷ 4$$\frac{1}{3}$$
= 1 ÷ {[(4 × 3) + 1] ÷ 3}
= 1 ÷ [(12 + 1) ÷ 3]
= 1 ÷ $$\frac{13}{3}$$
= 1 × $$\frac{3}{13}$$
= $$\frac{3}{13}$$

d. 9 ÷ 1$$\frac{2}{3}$$
Simplest form of 9 ÷ 1$$\frac{2}{3}$$ is $$\frac{27}{5}$$ or 5$$\frac{2}{5}$$.

Explanation:
9 ÷ 1$$\frac{2}{3}$$
= 9 ÷ {[(1 × 3) + 2] ÷ 3}
= 9 ÷ [(3+ 2) ÷ 3]
= 9 ÷ $$\frac{5}{3}$$
= 9 × $$\frac{3}{5}$$
= $$\frac{27}{5}$$ or 5$$\frac{2}{5}$$

Divide. Write answers in simplest form.

Question 1.
a. 1$$\frac{3}{4}$$ ÷ $$\frac{2}{3}$$ =
Simplest form of 1$$\frac{3}{4}$$ ÷ $$\frac{2}{3}$$ is $$\frac{21}{8}$$ or 2$$\frac{5}{8}$$.

Explanation:
1$$\frac{3}{4}$$ ÷ $$\frac{2}{3}$$
= {[(1 × 4) + 3] ÷ 4} ÷ $$\frac{2}{3}$$
=  [(4 + 3) ÷ 4] ÷ $$\frac{2}{3}$$
= $$\frac{7}{4}$$ ÷ $$\frac{2}{3}$$
= $$\frac{7}{4}$$ × $$\frac{3}{2}$$
= $$\frac{21}{8}$$ or 2$$\frac{5}{8}$$

b. 9 ÷ 1$$\frac{2}{3}$$ =
Simplest form of 9 ÷ 1$$\frac{2}{3}$$ is $$\frac{27}{5}$$ or 5$$\frac{2}{5}$$.

Explanation:
9 ÷ 1$$\frac{2}{3}$$
= 9 ÷ {[(1 × 3) + 2] ÷ 3}
= 9 ÷ [(3 + 2) ÷ 3]
= 9 ÷ $$\frac{5}{3}$$
= 9 × $$\frac{3}{5}$$
= $$\frac{27}{5}$$ or 5$$\frac{2}{5}$$

c. $$\frac{4}{9}$$ ÷ 1$$\frac{3}{5}$$ =
Simplest form of $$\frac{4}{9}$$ ÷ 1$$\frac{3}{5}$$ is $$\frac{5}{18}$$.

Explanation:
$$\frac{4}{9}$$ ÷ 1$$\frac{3}{5}$$
= $$\frac{4}{9}$$ ÷ {[(1 × 5) + 3] ÷ 5}
= $$\frac{4}{9}$$ ÷ [(5 + 3) ÷ 5]
= $$\frac{4}{9}$$ ÷ $$\frac{8}{5}$$
= $$\frac{4}{9}$$ × $$\frac{5}{8}$$
= $$\frac{1}{9}$$ × $$\frac{5}{2}$$
= $$\frac{5}{18}$$

d. 4$$\frac{1}{4}$$ ÷ 6 =
Simplest form of 4$$\frac{1}{4}$$ ÷ 6 is $$\frac{3}{4}$$.

Explanation:
4$$\frac{1}{4}$$ ÷ 6
= {[(4 × 4) + 1] ÷ 4} ÷ 6
= [(17 + 1) ÷ 4] ÷ 6
= $$\frac{18}{4}$$ ÷ 6
= $$\frac{18}{4}$$ × $$\frac{1}{6}$$
= $$\frac{3}{4}$$ × $$\frac{1}{1}$$
= $$\frac{3}{4}$$

Question 2.
a. 1$$\frac{5}{6}$$ ÷ $$\frac{1}{3}$$ =
Simplest form of 1$$\frac{5}{6}$$ ÷ $$\frac{1}{3}$$ is $$\frac{11}{2}$$ or 5$$\frac{1}{2}$$.

Explanation:
1$$\frac{5}{6}$$ ÷ $$\frac{1}{3}$$
= {[(1 × 6) + 5] ÷ 6} ÷ $$\frac{1}{3}$$
= [(6 + 5) ÷ 6] ÷ $$\frac{1}{3}$$
= $$\frac{11}{6}$$ ÷ $$\frac{1}{3}$$
= $$\frac{11}{6}$$ × $$\frac{3}{1}$$
= $$\frac{11}{2}$$ × $$\frac{1}{1}$$
= $$\frac{11}{2}$$ or 5$$\frac{1}{2}$$

b. 2$$\frac{2}{3}$$ ÷ $$\frac{1}{4}$$ =
Simplest form of 2$$\frac{2}{3}$$ ÷ $$\frac{1}{4}$$ is $$\frac{22}{3}$$ or 7$$\frac{1}{3}$$.

Explanation:
2$$\frac{2}{3}$$ ÷ $$\frac{1}{4}$$
= {[(2 × 3) + 2] ÷ 3} ÷ $$\frac{1}{4}$$
= [(6 + 5) ÷ 6] ÷ $$\frac{1}{4}$$
= $$\frac{11}{6}$$ ÷ $$\frac{1}{4}$$
= $$\frac{11}{6}$$ × $$\frac{4}{1}$$
= $$\frac{11}{3}$$ × $$\frac{2}{1}$$
= $$\frac{22}{3}$$ or 7$$\frac{1}{3}$$

c. $$\frac{4}{7}$$ ÷ 1$$\frac{3}{4}$$ =
Simplest form of $$\frac{4}{7}$$ ÷ 1$$\frac{3}{4}$$ is $$\frac{24}{77}$$.

Explanation:
$$\frac{4}{7}$$ ÷ 1$$\frac{3}{4}$$
= $$\frac{4}{7}$$ ÷ {[(2 × 3) + 2] ÷ 3}
= $$\frac{4}{7}$$ ÷ [(6 + 5) ÷ 6]
= $$\frac{4}{7}$$ ÷ $$\frac{11}{6}$$
= $$\frac{4}{7}$$ × $$\frac{6}{11}$$
= $$\frac{24}{77}$$

d. 2$$\frac{5}{6}$$ ÷ 1$$\frac{2}{5}$$ =
Simplest form of 2$$\frac{5}{6}$$ ÷ 1$$\frac{2}{5}$$ is $$\frac{85}{42}$$ or 2$$\frac{1}{85}$$.

Explanation:
2$$\frac{5}{6}$$ ÷ 1$$\frac{2}{5}$$
= {[(2 × 6) + 5] ÷ 6} ÷ {[(1 × 5) + 2] ÷ 5}
= [(12 + 5) ÷ 6]  ÷ [(5 + 2) ÷ 5]
= $$\frac{17}{6}$$ ÷ $$\frac{7}{5}$$
= $$\frac{17}{6}$$ × $$\frac{5}{7}$$
= $$\frac{85}{42}$$ or 2$$\frac{1}{85}$$

Question 3.
a. 3$$\frac{1}{4}$$ ÷ 4 =
Simplest form of 3$$\frac{1}{4}$$ ÷ 4 is $$\frac{13}{16}$$.

Explanation:
3$$\frac{1}{4}$$ ÷ 4
= {[(3 × 4) + 1] ÷ 4} ÷ 4
= [(12 + 1) ÷ 4]  ÷ 4
= $$\frac{13}{4}$$ ÷ 4
= $$\frac{13}{4}$$ × $$\frac{1}{4}$$
= $$\frac{13}{16}$$

b. 3$$\frac{2}{7}$$ ÷ 4$$\frac{1}{3}$$ =
Simplest form of 3$$\frac{2}{7}$$ ÷ 4$$\frac{1}{3}$$ is $$\frac{69}{91}$$.

Explanation:
3$$\frac{2}{7}$$ ÷ 4$$\frac{1}{3}$$
= {[(3 × 7) + 2] ÷ 7} ÷ {[(4 × 3) + 1] ÷ 3}
= [(21 + 2) ÷ 7]  ÷ [(12 + 1) ÷ 3]
= $$\frac{23}{7}$$ ÷ $$\frac{13}{3}$$
= $$\frac{23}{7}$$ × $$\frac{3}{13}$$
= $$\frac{69}{91}$$

c. 4$$\frac{4}{5}$$ ÷ 4$$\frac{1}{2}$$ =
Simplest form of 4$$\frac{4}{5}$$ ÷ 4$$\frac{1}{2}$$ is $$\frac{48}{45}$$ or 1$$\frac{3}{45}$$.

Explanation:
4$$\frac{4}{5}$$ ÷ 4$$\frac{1}{2}$$
= {[(4 × 5) + 4] ÷ 5} ÷ {[(4 × 2) + 1] ÷ 2}
= [(20 + 4) ÷ 5]  ÷ [(8 + 1) ÷ 2]
= $$\frac{24}{5}$$ ÷ $$\frac{9}{2}$$
= $$\frac{24}{5}$$ × $$\frac{2}{9}$$
= $$\frac{48}{45}$$ or 1$$\frac{3}{45}$$

Question 4.
a. 3$$\frac{1}{5}$$ ÷ 4$$\frac{3}{7}$$ =
Simplest form of 3$$\frac{1}{5}$$ ÷ 4$$\frac{3}{7}$$ is $$\frac{112}{155}$$.

Explanation:
3$$\frac{1}{5}$$ ÷ 4$$\frac{3}{7}$$
= {[(3 × 5) + 1] ÷ 5} ÷ {[(4 × 7) + 3] ÷ 7}
= [(15 + 1) ÷ 5]  ÷ [(28 + 3) ÷ 7]
= $$\frac{16}{5}$$ ÷ $$\frac{31}{7}$$
= $$\frac{16}{5}$$ × $$\frac{7}{31}$$
= $$\frac{112}{155}$$

b. 2$$\frac{8}{9}$$ ÷ 3$$\frac{4}{5}$$ =
Simplest form of 2$$\frac{8}{9}$$ ÷ 3$$\frac{4}{5}$$ is $$\frac{130}{171}$$.

Explanation:
2$$\frac{8}{9}$$ ÷ 3$$\frac{4}{5}$$
= {[(2 × 9) + 8] ÷ 9} ÷ {[(3 × 5) + 4] ÷ 5}
= [(18 + 8) ÷ 9]  ÷ [(15 + 4) ÷ 5]
= $$\frac{26}{9}$$ ÷ $$\frac{19}{5}$$
= $$\frac{26}{9}$$ × $$\frac{5}{19}$$
= $$\frac{130}{171}$$

c. 2$$\frac{1}{6}$$ ÷ 4$$\frac{1}{9}$$ =
Simplest form of 2$$\frac{1}{6}$$ ÷ 4$$\frac{1}{9}$$ is $$\frac{39}{74}$$.

Explanation:
2$$\frac{1}{6}$$ ÷ 4$$\frac{1}{9}$$
= {[(2 × 6) + 1] ÷ 6} ÷ {[(4 × 9) + 1] ÷ 9}
= [(12 + 1) ÷ 6]  ÷ [(36 + 1) ÷ 9]
= $$\frac{13}{6}$$ ÷ $$\frac{37}{9}$$
= $$\frac{13}{6}$$ × $$\frac{9}{37}$$
= $$\frac{13}{2}$$ × $$\frac{3}{37}$$
= $$\frac{39}{74}$$

d. 3$$\frac{1}{2}$$ ÷ 3$$\frac{1}{4}$$ =
Simplest form of 3$$\frac{1}{2}$$ ÷ 3$$\frac{1}{4}$$ is $$\frac{14}{13}$$ or 1$$\frac{1}{13}$$.

Explanation:
3$$\frac{1}{2}$$ ÷ 3$$\frac{1}{4}$$
= {[(3 × 2) + 1] ÷ 2} ÷ {[(3 × 4) + 1] ÷ 4}
= [(6 + 1) ÷ 2]  ÷ [(12 + 1) ÷ 4]
= $$\frac{7}{2}$$ ÷ $$\frac{13}{4}$$
= $$\frac{7}{2}$$ × $$\frac{4}{13}$$
= $$\frac{7}{1}$$ × $$\frac{2}{13}$$
= $$\frac{14}{13}$$ or 1$$\frac{1}{13}$$

Question 5.
a. 5$$\frac{2}{5}$$ ÷ 3$$\frac{1}{3}$$ =
Simplest form of 5$$\frac{2}{5}$$ ÷ 3$$\frac{1}{3}$$ is $$\frac{81}{50}$$ or 1$$\frac{31}{50}$$.

Explanation:
5$$\frac{2}{5}$$ ÷ 3$$\frac{1}{3}$$
= {[(5 × 5) + 2] ÷ 5} ÷ {[(3 × 3) + 1] ÷ 3}
= [(25 + 2) ÷ 5]  ÷ [(9 + 1) ÷ 3]
= $$\frac{27}{5}$$ ÷ $$\frac{10}{3}$$
= $$\frac{27}{5}$$ × $$\frac{3}{10}$$
= $$\frac{81}{50}$$ or 1$$\frac{31}{50}$$

b. 7 ÷ 2$$\frac{3}{8}$$ =
Simplest form of 7 ÷ 2$$\frac{3}{8}$$ is $$\frac{56}{19}$$ or 2$$\frac{18}{19}$$.

Explanation:
7 ÷ 2$$\frac{3}{8}$$
= 7 ÷ {[(2 × 8) + 3] ÷ 8}
= 7 ÷ [(16 + 3) ÷ 8]
= 7 ÷ $$\frac{19}{8}$$
= 7 × $$\frac{8}{19}$$
= $$\frac{56}{19}$$ or 2$$\frac{18}{19}$$

c. 4$$\frac{2}{7}$$ ÷ 3$$\frac{1}{3}$$ =
Simplest form of 4$$\frac{2}{7}$$ ÷ 3$$\frac{1}{3}$$ is $$\frac{9}{7}$$ or 1$$\frac{2}{7}$$.

Explanation:
4$$\frac{2}{7}$$ ÷ 3$$\frac{1}{3}$$
= {[(4 × 7) + 2] ÷ 7} ÷ {[(3 × 3) + 1] ÷ 3}
= [(28 + 2) ÷ 7]  ÷ [(9 + 1) ÷ 3]
= $$\frac{30}{7}$$ ÷ $$\frac{10}{3}$$
= $$\frac{30}{7}$$ × $$\frac{3}{10}$$
= $$\frac{3}{7}$$ × $$\frac{3}{1}$$
= $$\frac{9}{7}$$ or 1$$\frac{2}{7}$$

d. 2$$\frac{2}{3}$$ ÷ 3$$\frac{6}{11}$$ =
Simplest form of 2$$\frac{2}{3}$$ ÷ 3$$\frac{6}{11}$$ is $$\frac{88}{117}$$.
2$$\frac{2}{3}$$ ÷ 3$$\frac{6}{11}$$
= $$\frac{8}{3}$$ ÷ $$\frac{39}{11}$$
= $$\frac{8}{3}$$ × $$\frac{11}{39}$$
= $$\frac{88}{117}$$