Select all the ratios that are equivalent to the ratio 12 : 3. explain how you know.
a. 6: 1
b. 1: 4
c. 4: 1
d. 24 : 6
e. 15: 6
f. 1,200 : 300
g. 112: 13

the answers are c, d, &f

Step-by-step explanation:

the equivalence to 12:3

1200:300. = 12:3 (reduce by 100)

12:3= 4:1 (reduce by 3)

24:6= 12:3 (reduce by 2)

The ratio 12: 3 between two quantities A and B means that 12 times A is 3 times B, or 12*A = 3*B.

Then, if we multiply both sides by the same number k, we got:

k*12*A = k*3*B

If K = 2, then 24*A = 6*B, so the option D; 24:6 is equivalent.

if K = 1/3, then: 4*A = B, so the option C; 4:1 is equivalent.

if k = 100, then : 1200*A = 300*B, so the option F; 1200:300 is equivalent.

You can notice that in all the cases the ratio 12:3 is multiplied in both sides by the same number k, this is the relation you need to search for.

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range