Question

Sort the ratios listed at the right into bins so that equivalent ratios are grouped together:

(Ratios)
40:64 - 5/75 - 14:35 - 24:64 - 6/15 - 65/104 - 66/176 - 12/30 - 15:225 - 6/16 - 15:24 - 48:128
and there are 4 bins.

Answer 1

First bin: 40:64, 65/104,6/16
Second bin: 5/75, 15:225
Third bin: 14:35,6/15,12/30
Fourth bin: 24:64,66/176, 48:128

Answer 2

Step
`1`

Find the irreducible fraction in each ratio

case 1)
`(40)/(64)`

Divide by
`8` boths numerator and denominator

`(40)/(64)=(5)/(8)`

case 2)
`(5)/(75)`

Divide by
`5` boths numerator and denominator

`(5)/(75)=(1)/(15)`

case 3)
`(14)/(35)`

Divide by
`7` boths numerator and denominator

`(14)/(35)=(2)/(5)`

case 4)
`(24)/(64)`

Divide by
`8` boths numerator and denominator

`(24)/(64)=(3)/(8)`

case 5)
`(6)/(15)`

Divide by
`3` boths numerator and denominator

`(6)/(15)=(2)/(5)`

case 6)
`(65)/(104)`

Divide by
`13` boths numerator and denominator

`(65)/(104)=(5)/(8)`

case 7)
`(66)/(176)`

Divide by
`22` boths numerator and denominator

`(66)/(176)=(3)/(8)`

case 8)
`(12)/(30)`

Divide by
`6` boths numerator and denominator

`(12)/(30)=(2)/(5)`

case 9)
`(15)/(225)`

Divide by
`15` boths numerator and denominator

`(15)/(225)=(1)/(15)`

case 10)
`(6)/(16)`

Divide by
`2` boths numerator and denominator

`(6)/(16)=(3)/(8)`

case 11)
`(15)/(24)`

Divide by
`3` boths numerator and denominator

`(15)/(24)=(5)/(8)`

case 12)
`(48)/(128)`

Divide by
`16` boths numerator and denominator

`(48)/(128)=(3)/(8)`

Step
`2`

Sort the ratios into bins

1) First Bin

`Ratio=(5)/(8)`

`(40)/(64)`

`(65)/(104)`

`(15)/(24)`

2) Second Bin

`Ratio=(1)/(15)`

`(5)/(75)`

`(15)/(225)`

3) Third Bin

`Ratio=(2)/(5)`

`(14)/(35)`

`(6)/(15)`

`(12)/(30)`

4) Fourth Bin

`Ratio=(3)/(8)`

`(24)/(64)`

`(66)/(176)`

`(6)/(16)`

`(48)/(128)`