Question

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

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)  $\frac{40}{64}$

Divide by $8$ boths numerator and denominator

$\frac{40}{64}=\frac{5}{8}$

case 2)  $\frac{5}{75}$

Divide by $5$ boths numerator and denominator

$\frac{5}{75}=\frac{1}{15}$

case 3)  $\frac{14}{35}$

Divide by $7$ boths numerator and denominator

$\frac{14}{35}=\frac{2}{5}$

case 4)  $\frac{24}{64}$

Divide by $8$ boths numerator and denominator

$\frac{24}{64}=\frac{3}{8}$

case 5)  $\frac{6}{15}$

Divide by $3$ boths numerator and denominator

$\frac{6}{15}=\frac{2}{5}$

case 6)  $\frac{65}{104}$

Divide by $13$ boths numerator and denominator

$\frac{65}{104}=\frac{5}{8}$

case 7)  $\frac{66}{176}$

Divide by $22$ boths numerator and denominator

$\frac{66}{176}=\frac{3}{8}$

case 8)  $\frac{12}{30}$

Divide by $6$ boths numerator and denominator

$\frac{12}{30}=\frac{2}{5}$

case 9)  $\frac{15}{225}$

Divide by $15$ boths numerator and denominator

$\frac{15}{225}=\frac{1}{15}$

case 10)  $\frac{6}{16}$

Divide by $2$ boths numerator and denominator

$\frac{6}{16}=\frac{3}{8}$

case 11)  $\frac{15}{24}$

Divide by $3$ boths numerator and denominator

$\frac{15}{24}=\frac{5}{8}$

case 12)  $\frac{48}{128}$

Divide by $16$ boths numerator and denominator

$\frac{48}{128}=\frac{3}{8}$

Step $2$

Sort the ratios into bins

1) First Bin

$Ratio=\frac{5}{8}$

$\frac{40}{64}$

$\frac{65}{104}$

$\frac{15}{24}$

2) Second Bin

$Ratio=\frac{1}{15}$

$\frac{5}{75}$

$\frac{15}{225}$

3) Third Bin

$Ratio=\frac{2}{5}$

$\frac{14}{35}$

$\frac{6}{15}$

$\frac{12}{30}$

4) Fourth Bin

$Ratio=\frac{3}{8}$

$\frac{24}{64}$

$\frac{66}{176}$

$\frac{6}{16}$

$\frac{48}{128}$