Question

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.

Answer 1

1) 2 2/7

2) 2 1/3

3) 5/12

4) 8 2/3

5) 2/3

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

Answer 2

We must convert the mixed numbers to improper fractions.

`2(2)/(3)=(2\cdot3+2)/(3)=(8)/(3)\\\\1(1)/(6)=(1\cdot6+1)/(6)=(7)/(6)\\\\2(2)/(3)/1(1)/(6)=(8)/(3)/(7)/(6)=(8)/(\\ot3_1)\cdot(\\ot6^2)/(7)=(16)/(7)=2(2)/(7)`

`6(2)/(3)=(6\cdot3+2)/(3)=(20)/(3)\\\\2(6)/(7)=(2\cdot7+6)/(7)=(20)/(7)\\\\6(2)/(3)/\2(6)/(7)=(20)/(3)/(20)/(7)=(20\!\!\!\!\!\diagup^1)/(3)\cdot(7)/(20\!\!\!\!\!\diagup_1)=(7)/(3)=2(1)/(3)`

`4(1)/(6)=(4\cdot6+1)/(6)=(25)/(6)\\\\4(1)/(6)/10=(25)/(6)/(10)/(1)=(25\!\!\!\!\!\diagup^5)/(6)\cdot(1)/(10\!\!\!\!\!\diagup_2)=(5)/(12)`

`6(1)/(2)=(6\cdot2+1)/(2)=(13)/(2)\\\\6(1)/(2)/(3)/(4)=(13)/(2)/(3)/(4)=(13)/(\\ot2_1)\cdot(\\ot4^2)/(3)=(26)/(3)=8(2)/(3)`

`3(3)/(4)=(3\cdot4+3)/(4)=(15)/(4)\\\\5(5)/(8)=(5\cdot8+5)/(8)=(45)/(8)\\\\3(3)/(4)/5(5)/(8)=(15)/(3)/(45)/(8)=(15\!\!\!\!\!\diagup^1)/(3)\cdot(8)/(45\!\!\!\!\!\diagup_3)=(8)/(9)`