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2 2/3 divided by 1 1/6 = ?

6 2/3 divided by 2 6/7 = ?

4 1/6 divided by 10 = ?

6 1/2 divided by 3/4 = ?

3 3/4 divided by 5 5/8 = ?

All answers must be in simplest form. Answer check I'm doing.

Respuesta :

gmany

We must convert the mixed numbers to improper fractions.

[tex]2\dfrac{2}{3}=\dfrac{2\cdot3+2}{3}=\dfrac{8}{3}\\\\1\dfrac{1}{6}=\dfrac{1\cdot6+1}{6}=\dfrac{7}{6}\\\\2\dfrac{2}{3}\div1\dfrac{1}{6}=\dfrac{8}{3}\div\dfrac{7}{6}=\dfrac{8}{\not3_1}\cdot\dfrac{\not6^2}{7}=\dfrac{16}{7}=2\dfrac{2}{7}[/tex]

[tex]6\dfrac{2}{3}=\dfrac{6\cdot3+2}{3}=\dfrac{20}{3}\\\\2\dfrac{6}{7}=\dfrac{2\cdot7+6}{7}=\dfrac{20}{7}\\\\6\dfrac{2}{3}\div\2\dfrac{6}{7}=\dfrac{20}{3}\div\dfrac{20}{7}=\dfrac{20\!\!\!\!\!\diagup^1}{3}\cdot\dfrac{7}{20\!\!\!\!\!\diagup_1}=\dfrac{7}{3}=2\dfrac{1}{3}[/tex]

[tex]4\dfrac{1}{6}=\dfrac{4\cdot6+1}{6}=\dfrac{25}{6}\\\\4\dfrac{1}{6}\div10=\dfrac{25}{6}\div\dfrac{10}{1}=\dfrac{25\!\!\!\!\!\diagup^5}{6}\cdot\dfrac{1}{10\!\!\!\!\!\diagup_2}=\dfrac{5}{12}[/tex]

[tex]6\dfrac{1}{2}=\dfrac{6\cdot2+1}{2}=\dfrac{13}{2}\\\\6\dfrac{1}{2}\div\dfrac{3}{4}=\dfrac{13}{2}\div\dfrac{3}{4}=\dfrac{13}{\not2_1}\cdot\dfrac{\not4^2}{3}=\dfrac{26}{3}=8\dfrac{2}{3}[/tex]

[tex]3\dfrac{3}{4}=\dfrac{3\cdot4+3}{4}=\dfrac{15}{4}\\\\5\dfrac{5}{8}=\dfrac{5\cdot8+5}{8}=\dfrac{45}{8}\\\\3\dfrac{3}{4}\div5\dfrac{5}{8}=\dfrac{15}{3}\div\dfrac{45}{8}=\dfrac{15\!\!\!\!\!\diagup^1}{3}\cdot\dfrac{8}{45\!\!\!\!\!\diagup_3}=\dfrac{8}{9}[/tex]

Answer:

1) 2 2/7

2) 2 1/3

3) 5/12

4) 8 2/3

5) 2/3

Step-by-step explanation:

1)   2 2/3 divided by 1 1/6 = 2 2/7

2 2/3= 8/3

1 1/6= 7/6

8/3÷7/6=

8/3* the reciprocal of 7/6=

8/3*6/7=

simplified=

16/7 or 2 2/7

2)   6 2/3 divided by 2 6/7=2 1/3

6 2/3=20/3

2 6/7=20/7

20/3÷20/7=

20/3* the reciprocal of 20/7=

20/3*7/20=

simplified=

7/3 or 2 1/3

3)   4 1/6 divided by 10=5/12

4 1/6=25/6

25/6÷10=

25/6* the reciprocal of 10=

25/6*1/10=

simplified=

5/12

4)   6 1/2 divided by 3/4=8 2/3

6 1/2=13/2

13/2÷3/4=

13/2* the reciprocal of 3/4=

13/2*3/4=

simplified=

26/3 or 8 2/3

5)   3 3/4 divided by 5 5/8=2/3

3 3/4=15/4

5 5/8=45/8

15/4÷45/8=

15/4* the reciprocal of 45/8=

15/4*8/45=

simplified=

2/3

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