Answer:
[tex]\frac{1}{7}=\frac{3}{21}[/tex]
[tex]\frac{7}{1}=\frac{21}{3}[/tex]
Step-by-step explanation:
Verify each case
case 1) [tex]\frac{1}{7}=\frac{3}{21}[/tex]
Multiply in cross and then compare both sides
[tex]1*21=7*3[/tex]
[tex]21=21[/tex] ----> is true
therefore
Is a valid proportion
case 2) [tex]\frac{1}{21}=\frac{3}{7}[/tex]
Multiply in cross and then compare both sides
[tex]7*1=21*3[/tex]
[tex]7=63[/tex] ----> is not true
therefore
Is not a valid proportion
case 3) [tex]\frac{7}{1}=\frac{3}{21}[/tex]
Multiply in cross and then compare both sides
[tex]21*7=1*3[/tex]
[tex]147=3[/tex] ----> is not true
therefore
Is not a valid proportion
case 4) [tex]\frac{7}{1}=\frac{21}{3}[/tex]
Multiply in cross and then compare both sides
[tex]3*7=1*21[/tex]
[tex]21=21[/tex] ----> is true
therefore
Is a valid proportion
case 5) [tex]\frac{1}{7}=\frac{21}{3}[/tex]
Multiply in cross and then compare both sides
[tex]3*1=7*21[/tex]
[tex]3=147[/tex] ----> is not true
therefore
Is not a valid proportion
